This Maple session accompanies the paper "Three quadrant walks by invariants" and considers the case of simple NSEW steps.The proofs are in Section 8. restart:

Functional equation. The series Cm(1/x) is negative in x K:=1-t*(1/x+1/y+x+y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJLR0YoLCYiIiJGLyomSSJ0R0YoRi8sKiokSSJ4R0YoISIiRi8qJEkieUdGKEY1Ri9GNEYvRjdGL0YvRjU3I0Yu

eqC:=-K*C(x,y)+1-t/y*Cm(1/x)-t/x*Cm(1/y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcUNHRigsKiomLCYiIiJGMSomSSJ0R0YoRjEsKiokSSJ4R0YoISIiRjEqJEkieUdGKEY3RjFGNkYxRjlGMUYxRjdGMS1JIkNHRig2JEY2RjlGMUY3RjFGMSooRjNGMUY5RjctSSNDbUdGKDYjRjVGMUY3KihGM0YxRjZGNy1GPzYjRjhGMUY3NyNGLg==

Cmser:=proc(n) local i: local res:res:=coeff(convert(Cser(n),polynom),y,0): add(coeff(res,x,-i)/x^i,i=1..n+2): end: Cser:=proc(n) option remember: if n=0 then 1 else normal(series(subs(C(x,y)=Cser(n-1),Cm(1/x)=Cmser(n-1),Cm(1/y)=subs(x=y,Cmser(n-1)),eqC+C(x,y)),t,n+1)): fi: end: map(expand,Cser(4));

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

Functional equation. The series Am(1/x) is negative in x K:=1-t*(1/x+1/y+x+y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJLR0YoLCYiIiJGLyomSSJ0R0YoRi8sKiokSSJ4R0YoISIiRi8qJEkieUdGKEY1Ri9GNEYvRjdGL0YvRjU3I0Yu

eqA:=-K*A(x,y)+2/3+1/(3*y^2)+1/(3*x^2)-t/y*Am(1/x)-t/x*Am(1/y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcUFHRigsLiomLCYiIiJGMSomSSJ0R0YoRjEsKiokSSJ4R0YoISIiRjEqJEkieUdGKEY3RjFGNkYxRjlGMUYxRjdGMS1JIkFHRig2JEY2RjlGMUY3IyIiIyIiJEYxKiYjRjFGP0YxKUY5Rj5GN0YxKiZGQUYxKUY2Rj5GN0YxKihGM0YxRjlGNy1JI0FtR0YoNiNGNUYxRjcqKEYzRjFGNkY3LUZHNiNGOEYxRjc3I0Yu

Amser:=proc(n) local i: local res:res:=coeff(convert(Aser(n),polynom),y,0): add(coeff(res,x,-i)/x^i,i=1..n+2): end: Aser:=proc(n) option remember: if n=0 then 1 else normal(series(subs(A(x,y)=Aser(n-1),Am(1/x)=Amser(n-1),Am(1/y)=subs(x=y,Amser(n-1)),eqA+A(x,y)),t,n+1)): fi: end: map(expand,Aser(4));

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

We separate in A the contribution of two regions U denotes the part of A above the diagonal, DD the diagonal itself User:=proc(n) local i,j: collect(add(add(coeff(coeff(convert(Aser(n),polynom),x,i),y,j)*x^(j-i-1)*y^(j),i=-n..j-1),j=0..n+4),t,normal): end: User(5);

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

Dser:=proc(n) local i: collect(add(coeff(coeff(convert(Aser(n),polynom),x,i),y,i)*y^(i),i=0..n+4),t,normal):end: Dser(3);

LCYjIiIjIiIkIiIiKiYsJiMiIzVGJUYmKiYjIiIlRiVGJkkieUc2IkYmRiZGJilJInRHRi9GJEYmRiY=

Aexpr:=DD(x*y)+1/x*U(1/x,x*y)+1/y*U(1/y,x*y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZBZXhwckdGKCwoLUkjRERHRig2IyomSSJ4R0YoIiIiSSJ5R0YoRjRGNComRjMhIiItSSJVR0YoNiQqJEYzRjdGMkY0RjQqJkY1RjctRjk2JCokRjVGN0YyRjRGNDcjRi4=

Steps:=x+y+1/x+1/y; tSteps:=expand(subs(y=y/x,x=1/x,Steps));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZTdGVwc0dGKCwqKiRJInhHRighIiIiIiIqJEkieUdGKEYxRjJGMEYyRjRGMjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSd0U3RlcHNHRigsKkkieEdGKCIiIiomSSJ5R0YoISIiRi9GM0YwKiRGL0YzRjAqJkYvRjBGMkYwRjA3I0Yu

Vpy:=coeff(tSteps, x,1);Vmy:=coeff(tSteps, x,-1);V0y:=coeff(tSteps, x,0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWcHlHRigsJiIiIkYvSSJ5R0YoRi83I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWbXlHRigsJiokSSJ5R0YoISIiIiIiRjJGMjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWMHlHRigiIiE3I0Yu

eqD:=-(1-t*V0y)*DD(y)+2/3+2*t*Vmy*U(0,y)-2*t/y*U(0,0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcURHRigsKi1JI0RER0YoNiNJInlHRighIiIjIiIjIiIkIiIiKipGNUY3SSJ0R0YoRjcsJiokRjJGM0Y3RjdGN0Y3LUkiVUdGKDYkIiIhRjJGN0Y3KipGNUY3RjlGN0YyRjMtRj02JEY/Rj9GN0YzNyNGLg==

eqU:=-x*U(x,y)+1/3*x^2+t*x*Vpy*DD(y)+t*tSteps*x*U(x,y)-t/y*subs(x=1/x,coeff(Steps,y,-1))*U(x,0)-t*Vmy*U(0,y)+t/y*U(0,0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcVVHRigsMComSSJ4R0YoIiIiLUkiVUdGKDYkRjBJInlHRihGMSEiIiomI0YxIiIkRjEpRjAiIiNGMUYxKipJInRHRihGMUYwRjEsJkYxRjFGNUYxRjEtSSNEREdGKDYjRjVGMUYxKipGPUYxLCpGMEYxKiZGNUY2RjBGNkYxKiRGMEY2RjEqJkYwRjFGNUYxRjFGMUYwRjFGMkYxRjEqKEY9RjFGNUY2LUYzNiRGMCIiIUYxRjYqKEY9RjEsJiokRjVGNkYxRjFGMUYxLUYzNiRGSkY1RjFGNiooRj1GMUY1RjYtRjM2JEZKRkpGMUYxNyNGLg==

eqUfinal:=collect(subs(isolate(eqD,U(0,y)),2*eqU*y),[U,DD],factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllcVVmaW5hbEdGKCwqKigiIiMiIiJJInRHRihGMS1JIlVHRig2JEkieEdGKCIiIUYxISIiKiYsLCoqRjBGMUYyRjEpRjZGMEYxKUkieUdGKEYwRjFGMSoqRjBGMUYyRjFGPEYxRj5GMUYxKihGMEYxRjJGMUY+RjFGMSooRjBGMUY2RjFGPkYxRjgqJkYwRjFGMkYxRjFGMS1GNDYkRjZGPkYxRjEqKCwoKipGMEYxRjJGMUY2RjFGPkYxRjEqKEYwRjFGMkYxRjZGMUYxRjFGOEYxRj5GMS1JI0RER0YoNiNGPkYxRjEqKCNGMCIiJEYxLCYqJEY8RjFGMUYxRjFGMUY+RjFGMTcjRi4=

n:=20: normal(series(subs( U(x,y)=User(n),U(0,y)=subs(x=0,User(n)), U(x,0)=subs(y=0,User(n)),U(0,0)=subs(x=0,y=0,User(n)), DD(y)=Dser(n),eqUfinal),t,n-1));

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIz4=

collect(coeff(eqUfinal,U(x,y))/x/y/2,t,expand)

LCYiIiIhIiIqJiwqSSJ4RzYiRiMqJkkieUdGKEYkRidGJEYjKiRGJ0YkRiMqJkYnRiNGKkYjRiNGI0kidEdGKEYjRiM=

Kt:=1-t*tSteps;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNLdEdGKCwmKiYsKkkieEdGKCIiIiomSSJ5R0YoISIiRjFGNUYyKiRGMUY1RjIqJkYxRjJGNEYyRjJGMkkidEdGKEYyRjVGMkYyNyNGLg==

eqQ:=-Kt*Q(x,y)+1-t/y/x*Q(x,0)-t/x/y*Q(0,y)+t/x/y*Q(0,0)-t/x*Q(0,y);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcVFHRigsLiomLCYqJiwqSSJ4R0YoIiIiKiZJInlHRighIiJGM0Y3RjQqJEYzRjdGNComRjNGNEY2RjRGNEY0SSJ0R0YoRjRGN0Y0RjRGNC1JIlFHRig2JEYzRjZGNEY3RjRGNCoqRjpGNEY2RjdGM0Y3LUY8NiRGMyIiIUY0RjcqKkY6RjRGM0Y3RjZGNy1GPDYkRkFGNkY0RjcqKkY6RjRGM0Y3RjZGNy1GPDYkRkFGQUY0RjQqKEY6RjRGM0Y3RkNGNEY3NyNGLg==

Qser:=proc(n) option remember: if n=0 then 1 else convert(normal(series(subs(Q(x,y)=Qser(n-1),Q(0,0)=subs(x=0,y=0,Qser(n-1)),Q(x,0)=subs(y=0,Qser(n-1)), Q(0,y)=subs(x=0,Qser(n-1)),eqQ+Q(x,y)),t,n+1)),polynom): fi: end: map(expand,Qser(4));

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

Two pairs of invariants. The first pair is rational (and will not be used) I0x:=x+1/x-t*x^2-t/x^2+2*t; collect(%,t,factor); J0y:=y/t/(1+y)^2+t*(1+y)^2/y;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRJMHhHRigsLEkieEdGKCIiIiokRi8hIiJGMComSSJ0R0YoRjApRi8iIiNGMEYyKiZGNEYwRjVGMkYyKiZGNkYwRjRGMEYwNyNGLg==

LCYqKiksJkkieEc2IiIiIkYoISIiIiIjRigpLCZGJkYoRihGKEYqRigpRiZGKkYpSSJ0R0YnRihGKSomLCYqJEYtRihGKEYoRihGKEYmRilGKA==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRKMHlHRigsJiooSSJ5R0YoIiIiSSJ0R0YoISIiKSwmRjFGMUYwRjEiIiNGM0YxKihGMkYxRjRGMUYwRjNGMTcjRi4=

ratio0:=factor((I0x-J0y)/Kt);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdyYXRpbzBHRigqKkkieEdGKCEiIiwsKihJInRHRigiIiIpRi8iIiNGNEkieUdGKEY0RjQqJkYzRjRGNUY0RjQqJkYzRjQpRjdGNkY0RjQqJkYzRjRGN0Y0RjQqJkYvRjRGN0Y0RjBGNEYzRjApLCZGNEY0RjdGNEY2RjA3I0Yu

decoupling of y fx:=-1/x; gy:=y/t/(1+y)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNmeEdGKCwkKiRJInhHRighIiJGMTcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNneUdGKCooSSJ5R0YoIiIiSSJ0R0YoISIiLCZGMEYwRi9GMEYyNyNGLg==

factor(x*y-fx-gy);factor(%/Kt);

KiosLCooSSJ0RzYiIiIiKUkieEdGJiIiI0YnKUkieUdGJkYqRidGJyooRiVGJ0YoRidGLEYnRicqJkYlRidGLEYnRicqJkYpRidGLEYnISIiRiVGJ0YnRilGMEYlRjAsJkYnRidGLEYnRjA=

LCQqKEkieUc2IiIiIkkidEdGJSEiIiwmRiZGJkYkRiZGKEYo

I1x:=t*Q(x,0)-fx;J1y:=-t*(1+y)*Q(0,y)+gy+t*Q(0,0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRJMXhHRigsJiomSSJ0R0YoIiIiLUkiUUdGKDYkSSJ4R0YoIiIhRjFGMSokRjUhIiJGMTcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRKMXlHRigsKCooSSJ0R0YoIiIiLCZGMUYxSSJ5R0YoRjFGMS1JIlFHRig2JCIiIUYzRjEhIiIqKEYzRjFGMEY4RjJGOEYxKiZGMEYxLUY1NiRGN0Y3RjFGMTcjRi4=

factor(I1x-J1y); factor(subs(isolate(eqQ,Q(x,0)),%))

KiosNioqLUkiUUc2IjYkIiIhSSJ5R0YnIiIiKUkidEdGJyIiI0YrSSJ4R0YnRispRipGLkYrRisqKkYsRistRiY2JEYvRilGK0YvRitGKkYrRisqLEYuRitGJUYrRixGK0YvRitGKkYrRisqKkYsRistRiY2JEYpRilGK0YvRitGKkYrISIiKihGLEYrRjJGK0YvRitGKyooRixGK0YlRitGL0YrRisqKEYsRitGNkYrRi9GK0Y4KiZGKkYrRi1GK0YrKiZGL0YrRipGK0Y4Ri1GK0YrRi9GOEYtRjgsJkYrRitGKkYrRjg=

KiwsLCooSSJ0RzYiIiIiKUkieEdGJiIiI0YnKUkieUdGJkYqRidGJyooRiVGJ0YoRidGLEYnRicqJkYlRidGLEYnRicqJkYpRidGLEYnISIiRiVGJ0YnLCgqKi1JIlFHRiY2JEYpRixGJ0YlRidGKUYnRixGJ0YnKihGM0YnRiVGJ0YpRidGJ0YnRidGJ0YpRjBGJUYwLCZGJ0YnRixGJ0Yw

ratio1:=factor(%/Kt);collect(%, Q,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdyYXRpbzFHRigsJCoqSSJ5R0YoIiIiLCgqKi1JIlFHRig2JEkieEdGKEYwRjFJInRHRihGMUY3RjFGMEYxRjEqKEY0RjFGOEYxRjdGMUYxRjFGMUYxRjghIiIsJkYxRjFGMEYxRjpGOjcjRi4=

LCYqKEkieEc2IiIiIkkieUdGJUYmLUkiUUdGJTYkRiRGJ0YmISIiKihGJ0YmSSJ0R0YlRissJkYmRiZGJ0YmRitGKw==

Steps:=x+y+1/x+1/y; tSteps:=expand(subs(y=y/x,x=1/x,Steps));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZTdGVwc0dGKCwqKiRJInhHRighIiIiIiIqJEkieUdGKEYxRjJGMEYyRjRGMjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSd0U3RlcHNHRigsKkkieEdGKCIiIiomSSJ5R0YoISIiRi9GM0YwKiRGL0YzRjAqJkYvRjBGMkYwRjA3I0Yu

Vpy:=coeff(tSteps, x,1);Vmy:=coeff(tSteps, x,-1);V0y:=coeff(tSteps, x,0);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWcHlHRigsJiIiIkYvSSJ5R0YoRi83I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWbXlHRigsJiokSSJ5R0YoISIiIiIiRjJGMjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWMHlHRigiIiE3I0Yu

co:=t*V0y+2*t*x*Vpy-1;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjb0dGKCwmKioiIiMiIiJJInhHRihGMUkidEdGKEYxLCZGMUYxSSJ5R0YoRjFGMUYxRjEhIiI3I0Yu

eqUfinal

LCoqKCIiIyIiIkkidEc2IkYlLUkiVUdGJzYkSSJ4R0YnIiIhRiUhIiIqJiwsKipGJEYlRiZGJSlGK0YkRiUpSSJ5R0YnRiRGJUYlKipGJEYlRiZGJUYxRiVGM0YlRiUqKEYkRiVGJkYlRjNGJUYlKihGJEYlRitGJUYzRiVGLSomRiRGJUYmRiVGJUYlLUYpNiRGK0YzRiVGJSooLCgqKkYkRiVGJkYlRitGJUYzRiVGJSooRiRGJUYmRiVGK0YlRiVGJUYtRiVGM0YlLUkjRERHRic2I0YzRiVGJSooI0YkIiIkRiUsJiokRjFGJUYlRiVGJUYlRjNGJUYl

The new initial term ct:=(2/3)*(x^2+1)*y

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjdEdGKCwkKigjIiIjIiIkIiIiLCYqJClJInhHRihGMUYzRjNGM0YzRjNJInlHRihGM0YzNyNGLg==

Ysol:=factor([solve(1-t*tSteps,y)])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVZc29sR0YoNyQsJCoqIyIiIiIiI0YySSJ0R0YoISIiKUkieEdGKEYzRjUsKiomRjRGMkY2RjJGNUY0RjVGN0YyKiQpKiYsKkY5RjIqKEYzRjJGNEYyRjdGMkYyRjRGMkY3RjVGMiwqRjlGMkY+RjVGNEYyRjdGNUYyRjFGMkYyRjJGMiwkKipGMUYyLCpGOUYyRjpGMkY0RjJGN0Y1RjJGNEY1RjZGNUY1NyNGLg==

Gform:=proc(d,e,f) local i: add(a[i]*y^i,i=0..d)+add(b[i]/(y-beta[i]),i=1..e) +add(c[i]/(y-gamma[i])^2,i=1..f): end: Gform(2,3,4)

LDYqJiZJImFHNiI2IyIiIyIiIilJInlHRiZGKEYpRikqJiZGJTYjRilGKUYrRilGKSZGJTYjIiIhRikqJiZJImJHRiZGLkYpLCZGK0YpJkklYmV0YUdGJkYuISIiRjhGKSomJkY0RidGKSwmRitGKSZGN0YnRjhGOEYpKiYmRjQ2IyIiJEYpLCZGK0YpJkY3Rj9GOEY4RikqJiZJImNHRiZGLkYpKSwmRitGKSZJJmdhbW1hRyUqcHJvdGVjdGVkR0YuRjhGKEY4RikqJiZGRUYnRikpLCZGK0YpJkZJRidGOEYoRjhGKSomJkZFRj9GKSksJkYrRikmRklGP0Y4RihGOEYpKiYmRkU2IyIiJUYpKSwmRitGKSZGSUZXRjhGKEY4Rik=

d:=-1: e:=1: f:=1:collect(numer(factor(expand(rationalize(subs(y=Ysol[1],co*Gform(d,e,f)-ct)-subs(y=Ysol[2],co*Gform(d,e,f)-ct))))/sqrt((t*x^2+2*t*x+t-x)*(t*x^2-2*t*x+t-x))),x,factor): coeffs(%,x): sol:=solve({%}, [seq(a[i], i=0..d), seq(b[i], i=1..e), seq(beta[i], i=1..e), seq(c[i], i=1..f), seq(gamma[i], i=1..f)])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig3IzcmLyZJImJHRig2IyIiIiwkKiYjIiIjIiIkRjQpSSJ0R0YoRjghIiJGNC8mSSViZXRhR0YoRjNGPC8mSSJjR0YoRjMsJEY2RjwvJkkmZ2FtbWFHRiZGM0Y8NyNGLg==

Gform(d,e,f)

LCYqJiZJImJHNiI2IyIiIkYoLCZJInlHRiZGKCZJJWJldGFHRiZGJyEiIkYtRigqJiZJImNHRiZGJ0YoKSwmRipGKCZJJmdhbW1hRyUqcHJvdGVjdGVkR0YnRi0iIiNGLUYo

Gy:=subs(op(1,sol),Gform(d,e,f)); Gy:=factor(Gy)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHeUdGKCwmKigjIiIjIiIkIiIiKUkidEdGKEYxISIiLCZGM0YzSSJ5R0YoRjNGNkYzKihGMEYzRjRGNilGN0YxRjZGNjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHeUdGKCwkKiojIiIjIiIkIiIiSSJ5R0YoRjMpSSJ0R0YoRjEhIiIpLCZGM0YzRjRGM0YxRjdGMzcjRi4=

The function F(x) Fx:=-factor(expand(rationalize(subs(y=Ysol[1], op(sol),-ct+co*Gform(d,e,f))))); expand(%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNGeEdGKCwkKiojIiIjIiIkIiIiLCgqJkkidEdGKEYzKUkieEdGKEYxRjNGM0Y2RjNGOCEiIkYzRjZGOUY3RjlGOTcjRi4=

LCgjIiIjIiIkISIiKiZGIyIiIilJInhHNiJGJEYmRiYqKEYjRihGKkYmSSJ0R0YrRiZGKA==

Solution of the decoupling problem Fx:=-2*(t*x^2 + t - x)/(3*t*x^2); expand(%*3/2); Gy:=(2*y)/(3*t^2*(1 + y)^2);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNGeEdGKCwkKiojIiIjIiIkIiIiLCgqJkkidEdGKEYzKUkieEdGKEYxRjNGM0Y2RjNGOCEiIkYzRjZGOUY3RjlGOTcjRi4=

LCgiIiIhIiIqJClJInhHNiIiIiNGJEYkKiZGJ0YkSSJ0R0YoRiRGIw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHeUdGKCwkKiojIiIjIiIkIiIiSSJ5R0YoRjMpSSJ0R0YoRjEhIiIpLCZGM0YzRjRGM0YxRjdGMzcjRi4=

factor(ct-Gy*co-Fx);Hxy:=factor(%/Kt)

LCQqLiMiIiMiIiQiIiIsLCooSSJ0RzYiRicpSSJ4R0YrRiVGJylJInlHRitGJUYnRicqKEYqRidGLEYnRi9GJ0YnKiZGKkYnRi9GJ0YnKiZGLUYnRi9GJyEiIkYqRidGJywsRjBGJyomRipGJ0YsRidGJ0YxRidGKkYnRi1GM0YnKUYqRiVGMyksJkYnRidGL0YnRiVGM0YsRjNGJw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRIeHlHRigsJCouIyIiIyIiJCIiIkkieUdGKEYzSSJ4R0YoISIiLCwqKEkidEdGKEYzKUY1RjFGM0Y0RjNGMyomRjlGM0Y6RjNGMyomRjlGM0Y0RjNGM0Y5RjNGNUY2RjMpRjlGMUY2KSwmRjNGM0Y0RjNGMUY2RjY3I0Yu

op(3,numer(%))

LCwqKEkidEc2IiIiIilJInhHRiUiIiNGJkkieUdGJUYmRiYqJkYkRiZGJ0YmRiYqJkYkRiZGKkYmRiZGJEYmRighIiI=

Hpap:=2/3*y*(1-t*(1/x+y/x+x+x*y))/t^2/(1+y)^2

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVIcGFwR0YoLCQqLCMiIiMiIiQiIiJJInlHRihGMywmRjNGMyomSSJ0R0YoRjMsKiokSSJ4R0YoISIiRjMqJkY6RjtGNEYzRjNGOkYzKiZGOkYzRjRGM0YzRjNGO0YzKUY3RjFGOyksJkYzRjNGNEYzRjFGO0YzNyNGLg==

factor(Hpap/Hxy)

IiIi

Sy:=y*DD(y)+Gy;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNTeUdGKCwmKiZJInlHRigiIiItSSNEREdGKDYjRjBGMUYxKiojIiIjIiIkRjFGMEYxKUkidEdGKEY3ISIiKSwmRjFGMUYwRjFGN0Y7RjE3I0Yu

Rx:=2*t*subs(x=1/x,coeff(Steps, y, -1))*U(x,0)-Fx;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNSeEdGKCwmKigiIiMiIiJJInRHRihGMS1JIlVHRig2JEkieEdGKCIiIUYxRjEqKiNGMCIiJEYxLCgqJkYyRjEpRjZGMEYxRjFGMkYxRjYhIiJGMUYyRj5GPUY+RjE3I0Yu

Delta:=(1-t*V0y)^2-4*t^2*Vpy*Vmy;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZEZWx0YUdGKCwmIiIiRi8qKiIiJUYvKUkidEdGKCIiI0YvLCZGL0YvSSJ5R0YoRi9GLywmKiRGNiEiIkYvRi9GL0YvRjk3I0Yu

factor(Rx^2-Delta*Sy^2);

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

factor(subs(isolate(eqUfinal,U(x,0)),%)/Kt);denom(%)

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

LCQqKiIiKiIiIilJInhHNiIiIiRGJSlJInRHRigiIiVGJSksJkYlRiVJInlHRihGJUYsRiVGJQ==

factor(%%- (-4*t*x*Vpy*Sy^2+(Hxy-2*x*y*U(x,y))*((t*V0y+2*t*x*Vpy-1)*Sy+Rx)))

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

factor(subs(isolate(eqUfinal,U(x,0)),%));

IiIh

Sy;

LCYqJkkieUc2IiIiIi1JI0RER0YlNiNGJEYmRiYqKiMiIiMiIiRGJkYkRiYpSSJ0R0YlRiwhIiIpLCZGJkYmRiRGJkYsRjBGJg==

Rx;Delta;

LCYqKCIiIyIiIkkidEc2IkYlLUkiVUdGJzYkSSJ4R0YnIiIhRiVGJSoqI0YkIiIkRiUsKComRiZGJSlGK0YkRiVGJUYmRiVGKyEiIkYlRiZGM0YyRjNGJQ==

LCYiIiJGIyoqIiIlRiMpSSJ0RzYiIiIjRiMsJkYjRiNJInlHRihGI0YjLCYqJEYrISIiRiNGI0YjRiNGLg==

Ix:=Rx^2;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNJeEdGKCokKSwmKigiIiMiIiJJInRHRihGMy1JIlVHRig2JEkieEdGKCIiIUYzRjMqKiNGMiIiJEYzLCgqJkY0RjMpRjhGMkYzRjNGNEYzRjghIiJGM0Y0RkBGP0ZARjNGMkYzNyNGLg==

Jy:=Delta*Sy^2;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNKeUdGKComLCYiIiJGMCoqIiIlRjApSSJ0R0YoIiIjRjAsJkYwRjBJInlHRihGMEYwLCYqJEY3ISIiRjBGMEYwRjBGOkYwKSwmKiZGN0YwLUkjRERHRig2I0Y3RjBGMCoqI0Y1IiIkRjBGN0YwRjNGOilGNkY1RjpGMEY1RjA3I0Yu

Poles at 0 only for the x-invariants Ix;I1x;

KiQpLCYqKCIiIyIiIkkidEc2IkYnLUkiVUdGKTYkSSJ4R0YpIiIhRidGJyoqI0YmIiIkRicsKComRihGJylGLUYmRidGJ0YoRidGLSEiIkYnRihGNUY0RjVGJ0YmRic=

LCYqJkkidEc2IiIiIi1JIlFHRiU2JEkieEdGJSIiIUYmRiYqJEYqISIiRiY=

series(Ix,x,1);series(I1x,x,1);

KydJInhHNiIjIiIlIiIqISIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiISIk

KylJInhHNiIiIiIhIiIqJkkidEdGJEYlLUkiUUdGJDYkIiIhRixGJUYsLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiVGJQ==

Poles at y=-1 for J and J1. Note that J(y)=O(y), and J1(y)=O(y) Jy; J1y;

KiYsJiIiIkYkKioiIiVGJClJInRHNiIiIiNGJCwmRiRGJEkieUdGKUYkRiQsJiokRiwhIiJGJEYkRiRGJEYvRiQpLCYqJkYsRiQtSSNEREdGKTYjRixGJEYkKiojRioiIiRGJEYsRiRGJ0YvKUYrRipGL0YkRipGJA==

LCgqKEkidEc2IiIiIiwmRiZGJkkieUdGJUYmRiYtSSJRR0YlNiQiIiFGKEYmISIiKihGKEYmRiRGLUYnRi1GJiomRiRGJi1GKjYkRixGLEYmRiY=

series(Jy,y,1);series(J1y,y,1);

KyVJInlHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiJGKw==

KyVJInlHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiJGKw==

series(Jy,y=-1,1);series(J1y,y=-1,1);

KycsJiIiIkYkSSJ5RzYiRiQsJComIyIiJSIiKkYkKUkidEdGJkYqISIiRiQhIiUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGJCEiJA==

KycsJiIiIkYkSSJ5RzYiRiQsJCokSSJ0R0YmISIiRipGKi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0YkIiIh

We will ignore the rational pair and try to combine I,J and I1, J1 series(Ix-4/9*I1x^4,x,2)

KylJInhHNiIsJiomIyIiKSIiKiIiIkkidEdGJCEiIkYsKigjIiM7RilGKkYrRiotSSJRR0YkNiQiIiFGM0YqRiwhIiQsLCooI0YoIiIkRipGK0YqLUkiVUdGJEYyRipGKkYnRioqJiMiIiVGKUYqKUYrIiIjRixGKiooRi5GKkYrRiotLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YqNiNGMUYyRipGLCooRjdGKkY+RiopRjBGP0YqRiwhIiMtSSJPR0ZFRkhGLA==

A3:=coeff(%,x,-3)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNBM0dGKCwmKiYjIiIpIiIqIiIiSSJ0R0YoISIiRjUqKCMiIztGMkYzRjRGMy1JIlFHRig2JCIiIUY8RjNGNTcjRi4=

factor(series(Ix-4/9*I1x^4-A3*I1x^3,x,3))

KylJInhHNiIsJCooIyIiJSIiKiIiIiwuKigiIidGKilJInRHRiRGKEYqKS1JIlFHRiQ2JCIiIUY0IiIjRipGKiooRi1GKilGLyIiJEYqLUkiVUdGJEYzRipGKiooRihGKkY3RiotLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YqNiNGMkYzRiohIiIqKEYtRiopRi9GNUYqRjFGKkYqKiZGNUYqRkdGKkYqRipGKkYqRkdGRUYqISIjLCQqKCMiIilGKUYqLDAqKEYoRiopRjFGOEYqRi5GKkYqKihGOEYqRkdGKkYwRipGKiooRjhGKkZHRiotLUY+NiNGOkYzRipGKiomRkdGKi0tJkY/NiRGKkYqRkRGM0YqRkUqKEY4RipGL0YqRjlGKkZFKihGOEYqRi9GKkY8RipGKkYqRkVGKkYvRkVGKkZFLUkiT0dGQEZDRjQ=

A2:=coeff(%,x,-2); collect(%,[Q,U])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNBMkdGKCwkKigjIiIlIiIqIiIiLC4qKCIiJ0YzKUkidEdGKEYxRjMpLUkiUUdGKDYkIiIhRj0iIiNGM0YzKihGNkYzKUY4IiIkRjMtSSJVR0YoRjxGM0YzKihGMUYzRkBGMy0tJkkiREdGJTYjRjM2I0Y7RjxGMyEiIiooRjZGMylGOEY+RjNGOkYzRjMqJkY+RjNGTUYzRjNGM0YzRjNGTUZLRjM3I0Yu

LCwqKCMiIikiIiQiIiIpSSJ0RzYiIiIjRicpLUkiUUdGKjYkIiIhRjBGK0YnRicqJkYkRidGLUYnRicqKCMiIzsiIipGJ0YpRictLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRio2I0YnNiNGLkYvRichIiIqKEYkRidGKUYnLUkiVUdGKkYvRidGJyooIyIiJUY1RicsJiomRitGJ0YoRidGJ0YnRidGJ0YoRj9GJw==

factor(series(Ix-4/9*I1x^4-A3*I1x^3-A2*I1x^2,x,3))

KydJInhHNiIsJCooIyIiKSIiKiIiIiw4KigiIiNGKiktSSJRR0YkNiQiIiFGMiIiJEYqKUkidEdGJCIiJUYqISIiKioiIidGKi1JIlVHRiRGMUYqRi9GKilGNUYzRipGNyoqRjZGKkY8RipGL0YqLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKjYjRjBGMUYqRioqKEYzRiopRjVGLUYqKUYvRi1GKkY3KihGM0YqRkhGKi0tRkA2I0Y7RjFGKkYqKiZGSEYqLS0mRkE2JEYqRipGRkYxRipGNyooRi1GKkZIRipGL0YqRjcqKEYzRipGNUYqRjpGKkY3KihGM0YqRjVGKkY+RipGKkYvRjdGKkY3RipGNUY3RipGNy1JIk9HRkJGRUYy

A1:=coeff(%,x,-1);collect(%,[Q,U])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNBMUdGKCwkKigjIiIpIiIqIiIiLDgqKCIiI0YzKS1JIlFHRig2JCIiIUY7IiIkRjMpSSJ0R0YoIiIlRjMhIiIqKiIiJ0YzLUkiVUdGKEY6RjNGOEYzKUY+RjxGM0ZAKipGP0YzRkVGM0Y4RjMtLSZJIkRHRiU2I0YzNiNGOUY6RjNGMyooRjxGMylGPkY2RjMpRjhGNkYzRkAqKEY8RjNGTkYzLS1GSTYjRkRGOkYzRjMqJkZORjMtLSZGSjYkRjNGM0ZMRjpGM0ZAKihGNkYzRk5GM0Y4RjNGQCooRjxGM0Y+RjNGQ0YzRkAqKEY8RjNGPkYzRkdGM0YzRjhGQEYzRkBGM0Y+RkBGMzcjRi4=

LDIqKCMiIzsiIioiIiIpSSJ0RzYiIiIkRicpLUkiUUdGKjYkIiIhRjBGK0YnISIiKigjIiIpRitGJ0YpRicpRi0iIiNGJ0YxKiYsKCooIyIjS0YmRicpRilGNkYnLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YqNiNGJzYjRi5GL0YnRicqKCNGJUYrRidGPEYnLUkiVUdGKkYvRidGMSooI0Y0RiZGJywmKiZGNkYnRjxGJ0YxRidGMUYnRilGMUYnRidGLUYnRicqJkYzRidGPUYnRicqKEZLRidGKUYnLS0mRkA2JEYnRidGRUYvRidGMSomRjNGJ0ZIRidGMSooRjNGJ0YpRictLUY/NiNGSUYvRidGJyomRktGJ0YpRjFGMQ==

An invariant with no pole at 0 factor(series(Ix-4/9*I1x^4-A3*I1x^3-A2*I1x^2-A1*I1x,x,4))

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

What happened to the J-invariant meanwhile? factor(series(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y,y=-1,3))

KycsJiIiIkYkSSJ5RzYiRiQsJCooIyIiJSIiKkYkKUkidEdGJiIiIyEiIiwsKigiIidGJEYtRiQtSSJVR0YmNiQiIiFGNkYkRiQqKEYqRiRGLUYkLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGJDYjSSJRR0YmRjVGJEYvKiYiIiRGJC1JI0RER0YmNiNGL0YkRi8qJkYqRiQtRkE2JEY2Ri9GJEYkRi5GL0YkRi8hIiMtSSJPR0Y8Rj9GLw==

Dm1sol:=isolate(subs(y=-1,eqD),DD(-1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdEbTFzb2xHRigvLUkjRERHRig2IyEiIiwmKigiIiMiIiJJInRHRihGNi1JIlVHRig2JCIiIUY7RjZGNiNGNSIiJEY2NyNGLg==

factor(series(eqQ,y=-1,1))

KycsJiIiIkYkSSJ5RzYiRiQsJComLCoqJi1JIlFHRiY2JEkieEdGJiEiIkYkRi5GJEYkKiZJInRHRiZGJC1GLDYkRi4iIiFGJEYvKiZGMUYkLUYsNiRGNEY0RiRGJEYuRi9GJEYuRi9GL0Y0LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjRiRGJA==

series(op(1,%),x,2)

KydJInhHNiIsKC1JIlFHRiQ2JCIiISEiIkYqKiZJInRHRiQiIiItLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YtNiNGJzYkRilGKUYtRi1GLUYtRiktSSJPR0YyRjVGLQ==

Q0m1sol:=isolate(coeff(%,x,0),Q(0,-1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShRMG0xc29sR0YoLy1JIlFHRig2JCIiISEiIiwmKiZJInRHRigiIiItLSZJIkRHRiU2I0Y3NiNGMDYkRjJGMkY3RjdGN0Y3NyNGLg==

factor(subs(Q0m1sol,Dm1sol,series(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y,y=-1,4)))

KycsJiIiIkYkSSJ5RzYiRiQsJCooIyIiJSIiKkYkKUkidEdGJiIiIyEiIiwuKigiIidGJEYsRiQtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0YkNiNJIlVHRiY2JCIiIUY+RiRGJCooRi5GJEYsRiQtLSZGNjYkRiRGJDYjSSJRR0YmRj1GJEYvKihGMkYkRi1GJC1GPEY9RiRGLyooRipGJEYtRiQtLUY1RkRGPUYkRiQqJiIiJEYkLS1GNjYjSSNEREdGJjYjRi9GJEYkKiZGKkYkLS0mRjY2I0YuRkQ2JEY+Ri9GJEYvRiRGJEYvLUkiT0dGN0Y6Rj4=

series(eqD,y=-1,2); op(3,%);

KyksJiIiIkYkSSJ5RzYiRiQsKC1JI0RER0YmNiMhIiJGKyMiIiMiIiRGJCooRi1GJEkidEdGJkYkLUkiVUdGJjYkIiIhRjRGJEYkRjQsKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGKUYqRisqKEYtRiRGMEYkLUYyNiRGNEYrRiRGK0YvRiRGJC1JIk9HRjk2I0YkRi0=

LCgtLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSNEREdGKTYjISIiRi0qKCIiIyIiIkkidEdGKUYwLUkiVUdGKTYkIiIhRi1GMEYtKihGL0YwRjFGMC1GMzYkRjVGNUYwRjA=

Dm1diff:=isolate(%,(D(DD))(-1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShEbTFkaWZmR0YoLy0tSSJER0YlNiNJI0RER0YoNiMhIiIsJiooIiIjIiIiSSJ0R0YoRjktSSJVR0YoNiQiIiFGNUY5RjUqKEY4RjlGOkY5LUY8NiRGPkY+RjlGOTcjRi4=

factor(subs(Q0m1sol,Dm1sol,Dm1diff,series(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y,y=-1,4)))

KycsJiIiIkYkSSJ5RzYiRiQsJCooIyIiKSIiKkYkKUkidEdGJiIiIyEiIiwsKigiIiRGJEYsRiQtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0YkNiNJIlVHRiY2JCIiIUY+RiRGJComRixGJC0tJkY2NiRGJEYkNiNJIlFHRiZGPUYkRi8qKEYuRiRGLUYkLS1GNUZERj1GJEYkKihGMkYkRi1GJC1GPDYkRj5GL0YkRi8qJkYuRiQtLSZGNjYjRi5GREZLRiRGL0YkRiRGLy1JIk9HRjdGOkY+

factor(series(eqU,y=-1,1))

KycsJiIiIkYkSSJ5RzYiRiQsKiomSSJ4R0YmRiQtSSJVR0YmNiRGKSEiIkYkRi0qJiNGJCIiJEYkKUYpIiIjRiRGJComSSJ0R0YmRiQtRis2JEYpIiIhRiRGJComRjRGJC1GKzYkRjdGN0YkRi1GNy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0YkRiQ=

series(op(1,%),x,2)

KydJInhHNiIsJi1JIlVHRiQ2JCIiISEiIkYqKiZJInRHRiQiIiItLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YtNiNGJzYkRilGKUYtRi1GLS1JIk9HRjJGNSIiIw==

U0m1sol:=isolate(coeff(%,x,1),U(0,-1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShVMG0xc29sR0YoLy1JIlVHRig2JCIiISEiIiomSSJ0R0YoIiIiLS0mSSJER0YlNiNGNjYjRjA2JEYyRjJGNjcjRi4=

factor(subs(Q0m1sol,Dm1sol,Dm1diff,U0m1sol,series(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y,y=-1,4)))

KycsJiIiIkYkSSJ5RzYiRiQsJCooIyIiKSIiKkYkKUkidEdGJiIiIyEiIiwoKiZGLEYkLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiRGJEYkNiNJIlFHRiY2JCIiIUY9RiRGJCooRi5GJEYtRiQtLSZGNTYjRiRGOkY8RiRGLyomRi5GJC0tJkY1NiNGLkY6NiRGPUYvRiRGJEYkRi9GLy1JIk9HRjZGQkY9

factor(series(eqQ,y=-1,2))

KyksJiIiIkYkSSJ5RzYiRiQsJComLCoqJi1JIlFHRiY2JEkieEdGJiEiIkYkRi5GJEYkKiZJInRHRiZGJC1GLDYkRi4iIiFGJEYvKiZGMUYkLUYsNiRGNEY0RiRGJEYuRi9GJEYuRi9GL0Y0KiYsLiooRitGJEYxRiQpRi4iIiNGJEYkKiZGMUYkLUYsNiRGNEYvRiRGJComLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGPDYjRixGLUYkRi5GJEYvKiZGMUYkRitGJEYvRjBGJEY1Ri9GJEYuRi9GJC1JIk9HRkU2I0YkRjw=

op(3,%);

KiYsLiooLUkiUUc2IjYkSSJ4R0YnISIiIiIiSSJ0R0YnRispRikiIiNGK0YrKiZGLEYrLUYmNiQiIiFGKkYrRisqJi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjRi42I0YmRihGK0YpRitGKiomRixGK0YlRitGKiomRixGKy1GJjYkRilGMkYrRisqJkYsRistRiY2JEYyRjJGK0YqRitGKUYq

series(%,x,2)

KydJInhHNiIsKC0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIjNiNJIlFHRiQ2JCIiISEiIkYzKiYtLSZGKTYjIiIiRi9GMUY5SSJ0R0YkRjlGMyomRjpGOS1GNjYkRjJGMkY5RjlGMi1JIk9HRipGOEY5

diff2Q0m1:=isolate(op(1,%), (D[2](Q))(0, -1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpkaWZmMlEwbTFHRigvLS0mSSJER0YlNiMiIiM2I0kiUUdGKDYkIiIhISIiLCYqJi0tJkYyNiMiIiJGNUY3RkBJInRHRihGQEY5KiZGQUZALUY9NiRGOEY4RkBGQDcjRi4=

factor(subs(Q0m1sol,Dm1sol,Dm1diff,U0m1sol,diff2Q0m1,series(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y,y=-1,4)))

KycsJiIiIkYkSSJ5RzYiRiQsJCooIyIiKSIiKkYkSSJ0R0YmISIiLCYqJkYsRiQtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2JEYkRiQ2I0kiUUdGJjYkIiIhRjtGJEYtKiYiIiNGJC0tJkYzNiNGJEY4NiRGO0YtRiRGJEYkRiRGLS1JIk9HRjRGQUY7

factor(series(eqQ,x,3))

KylJInhHNiIsJComLCwqKEkidEdGJCIiIi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRio2I0kiUUdGJDYkIiIhSSJ5R0YkRipGN0YqISIiKiZGKUYqLUYsNiRGNkY2RipGKiomLUY0RjVGKkY3RipGKiomRilGKkYrRipGOEY3RjhGKkY3RjhGOEY2LCQqKCNGKiIiI0YqLC4qKkZCRipGKUYqRj1GKilGN0ZCRipGOCoqRkJGKkYpRipGPUYqRjdGKkY4KihGKUYqLS0mRi42JEYqRipGM0Y1RipGN0YqRjgqJkYpRiotRklGO0YqRioqJkYpRipGSEYqRjgqKEZCRipGK0YqRjdGKkYqRipGN0Y4RjhGKi1JIk9HRi9GMkZC

subs(y=-1,op(3,%))

LCYqKCMiIiIiIiNGJUkidEc2IkYlLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YoNiRGJUYlNiNJIlFHRig2JCIiIUY0RiVGJS0tJkYsNiNGJUYxNiRGNCEiIkY6

diff1Q0m1:=isolate(%,(D[1](Q))(0, -1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpkaWZmMVEwbTFHRigvLS0mSSJER0YlNiMiIiI2I0kiUUdGKDYkIiIhISIiLCQqKCNGNCIiI0Y0SSJ0R0YoRjQtLSZGMjYkRjRGNEY1NiRGOEY4RjRGNDcjRi4=

No pole in the y invariant either... factor(subs(Q0m1sol,Dm1sol,Dm1diff,U0m1sol,diff2Q0m1,diff1Q0m1,series(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y,y=-1,5)))

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

Let us check this using the known values of Q(x,0). This gives the first terms of the unknown series A, which seems to be zero n:=20: A0expser:=normal(series(subs(U(x,0)=subs(y=0,User(n)),Q(x,0)=subs(y=0,Qser(n)),Q(0,0)=subs(x=0,y=0,Qser(n)),U(0,0)=subs(x=0,y=0,User(n)),(D[1](Q))(0, 0)=coeff(coeff(Qser(n),x,1),y,0), (D[1](U))(0, 0)=coeff(coeff(User(n),x,1),y,0), (D[1, 1](Q))(0, 0)=2*coeff(coeff(Qser(n),x,2),y,0) ,(D[1, 1](U))(0, 0)=2*coeff(coeff(User(n),x,2),y,0) , Ix-4/9*I1x^4-A3*I1x^3-A2*I1x^2-A1*I1x),t,n));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlBMGV4cHNlckdGKCslSSJ0R0YoLUkiT0dGJTYjIiIiIiM9NyNGLg==

n:=20: normal(series(subs(DD(y)=Dser(n), Q(0,y)=subs(x=0,Qser(n)),Q(0,0)=subs(x=0,y=0,Qser(n)), Q(0,0)=subs(x=0,y=0,Qser(n)),U(0,0)=subs(x=0,y=0,User(n)),(D[1](Q))(0, 0)=coeff(coeff(Qser(n),x,1),y,0), (D[1](U))(0, 0)=coeff(coeff(User(n),x,1),y,0), (D[1, 1](Q))(0, 0)=2*coeff(coeff(Qser(n),x,2),y,0) ,(D[1, 1](U))(0, 0)=2*coeff(coeff(User(n),x,2),y,0) ,Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y),t,n));

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzs=

This is encouraging! Let us check that the ratio is a multiple of xy The factor Kt disappears from the denominator ratio:=factor(subs(isolate(eqUfinal,U(x,0)), isolate(eqQ,Q(x,0)), ((Ix-4/9*I1x^4-A3*I1x^3-A2*I1x^2-A1*I1x)-(Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y))/Kt)): denom(%)

LCQqKiIiKiIiIilJInRHNiIiIiNGJSksJkYlRiVJInlHRihGJUYpRiUpSSJ4R0YoRilGJUYl

factor(subs(isolate(eqD,DD(y)),series(ratio,x,2)))

KydJInhHNiIsJCosIyIjOyIiKiIiIiwsKihJInRHRiRGKi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRio2I0kiUUdGJDYkIiIhSSJ5R0YkRipGOkYqISIiKiZGLUYqLUYvNiRGOUY5RipGKiomLUY3RjhGKkY6RipGKiomRi1GKkYuRipGO0Y6RjtGKkYtRjtGOkYqLCZGKkYqRjpGKkY7RjtGOy1JIk9HRjJGNUY5

factor(series(eqQ,x,2))

KydJInhHNiIsJComLCwqKEkidEdGJCIiIi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRio2I0kiUUdGJDYkIiIhSSJ5R0YkRipGN0YqISIiKiZGKUYqLUYsNiRGNkY2RipGKiomLUY0RjVGKkY3RipGKiomRilGKkYrRipGOEY3RjhGKkY3RjhGOEY2LUkiT0dGL0YyRio=

diffQ0y:=isolate(op(1,%), (D[1](Q))(0, y))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShkaWZmUTB5R0YoLy0tJkkiREdGJTYjIiIiNiNJIlFHRig2JCIiIUkieUdGKComLCgqJkkidEdGKEY0LUYwNiRGOEY4RjQhIiIqJi1GNkY3RjRGOUY0RkBGOUY0RjQsJiomRj1GNEY5RjRGQEY9RkBGQDcjRi4=

factor(subs(isolate(eqD,DD(y)),diffQ0y,series(ratio,x,3)))

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

factor(series(eqU,x,2))

KydJInhHNiIqJiwuKigtSSNEREdGJDYjSSJ5R0YkIiIiSSJ0R0YkRiwpRisiIiNGLEYsKihGKEYsRi1GLEYrRixGLCooRi1GLC0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiw2I0kiVUdGJDYkIiIhRitGLEYrRixGLComRi1GLC1GMzYkRj1GPUYsISIiKiZGMkYsRi1GLEYsKiYtRjtGPEYsRitGLEZBRixGK0ZBRiwtSSJPR0Y2RjlGLw==

diffU0y:=isolate(op(1,%), (D[1](U))(0, y))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShkaWZmVTB5R0YoLy0tJkkiREdGJTYjIiIiNiNJIlVHRig2JCIiIUkieUdGKComLCoqKC1JI0RER0YoNiNGOUY0SSJ0R0YoRjQpRjkiIiNGNCEiIiooRj1GNEZARjRGOUY0RkMqJkZARjQtRjA2JEY4RjhGNEY0KiYtRjZGN0Y0RjlGNEY0RjQsJiomRkBGNEY5RjRGNEZARjRGQzcjRi4=

factor(subs(isolate(eqD,DD(y)),diffQ0y,diffU0y,isolate(eqD,DD(y)),series(ratio,x,3)))

KydJInhHNiIsJCosIyIiKSIiKiIiIiw4KioiIiNGKilJInRHRiRGLUYqLUkiUUdGJDYkIiIhSSJ5R0YkRiopRjQiIiRGKiEiIioqIiIlRipGMEYqRi5GKilGNEYtRipGNyooLS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiRGKkYqNiNGMUYyRipGLkYqRjpGKkY3KigtRj02JEYzRjNGKkYuRipGNEYqRioqKkYtRipGMEYqRi5GKkY0RipGNyoqRi1GKkY8RipGLkYqRjRGKkY3KipGLUYqLS0mRj82I0YqRkRGR0YqRi9GKkY0RipGKiomRi5GKkZGRipGKiooRi1GKkYwRipGOkYqRioqJkY8RipGLkYqRjcqJkYtRipGOkYqRjdGKkYuRjdGNEYqKSwmRipGKkY0RipGLUY3RjdGMy1JIk9HRkBGTkYq

factor(series(eqQ,x,3))

KylJInhHNiIsJComLCwqKEkidEdGJCIiIi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRio2I0kiUUdGJDYkIiIhSSJ5R0YkRipGN0YqISIiKiZGKUYqLUYsNiRGNkY2RipGKiomLUY0RjVGKkY3RipGKiomRilGKkYrRipGOEY3RjhGKkY3RjhGOEY2LCQqKCNGKiIiI0YqLC4qKkZCRipGKUYqRj1GKilGN0ZCRipGOCoqRkJGKkYpRipGPUYqRjdGKkY4KihGKUYqLS0mRi42JEYqRipGM0Y1RipGN0YqRjgqJkYpRiotRklGO0YqRioqJkYpRipGSEYqRjgqKEZCRipGK0YqRjdGKkYqRipGN0Y4RjhGKi1JIk9HRi9GMkZC

diffdiff1Q0y:=isolate(op(3,%),(D[1, 1](Q))(0, y))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS1kaWZmZGlmZjFRMHlHRigvLS0mSSJER0YlNiQiIiJGNDYjSSJRR0YoNiQiIiFJInlHRigqJiwqKioiIiNGNEkidEdGKEY0LUY2RjdGNClGOUY9RjRGNCoqRj1GNEY+RjRGP0Y0RjlGNEY0KiZGPkY0LUYwNiRGOEY4RjQhIiIqKEY9RjQtLSZGMjYjRjRGNUY3RjRGOUY0RkVGNCwmKiZGPkY0RjlGNEZFRj5GRUZFNyNGLg==

The ratio is a multiple of x factor(subs(isolate(eqD,DD(y)),diffQ0y,diffU0y,isolate(eqD,DD(y)),diffdiff1Q0y,diffQ0y,series(ratio,x,3)))

KyVJInhHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiJGKw==

and a multiple of y series(ratio,y,1)

KyVJInlHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiJGKw==

Ixnul:=Ix-4/9*I1x^4-A3*I1x^3-A2*I1x^2-A1*I1x-A0;

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

Jynul:=Jy-4/9*J1y^4-A3*J1y^3-A2*J1y^2-A1*J1y-A0

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

In fact, A0=0 factor(series(Jynul,y,1))

KydJInlHNiIsJEkjQTBHRiQhIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiJGLw==

One root is known (say B1, coming from Delta), another (denoted B0) is double Ixform:=Ix-4/9*(I1-B0)^2*(I1-B1)*(I1); Jyform:=Jy-4/9*(J1-B0)^2*(J1-B1)*(J1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdJeGZvcm1HRigsJiokKSwmKigiIiMiIiJJInRHRihGNC1JIlVHRig2JEkieEdGKCIiIUY0RjQqKiNGMyIiJEY0LCgqJkY1RjQpRjlGM0Y0RjRGNUY0RjkhIiJGNEY1RkFGQEZBRjRGM0Y0RjQqKiMiIiUiIipGNCksJkkjSTFHRihGNEkjQjBHRihGQUYzRjQsJkZIRjRJI0IxR0YoRkFGNEZIRjRGQTcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdKeWZvcm1HRigsJiomLCYiIiJGMSoqIiIlRjEpSSJ0R0YoIiIjRjEsJkYxRjFJInlHRihGMUYxLCYqJEY4ISIiRjFGMUYxRjFGO0YxKSwmKiZGOEYxLUkjRERHRig2I0Y4RjFGMSoqI0Y2IiIkRjFGOEYxRjRGOylGN0Y2RjtGMUY2RjFGMSoqI0YzIiIqRjEpLCZJI0oxR0YoRjFJI0IwR0YoRjtGNkYxLCZGS0YxSSNCMUdGKEY7RjFGS0YxRjs3I0Yu

with(gfun): Yser:=op(algeqtoseries(numer(Delta),t,y,17,true))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVZc2VyR0YoKzdJInRHRigiIiUiIiMiI0tGMCIkPyQiIiciJSVlJCIiKSImM0klIiM1IidzMWEiIzciKE8oR3EiIzkiKSFbO1AqIiM7IitHVGF1NyIjPS1JIk9HRiU2IyIiIiIjPjcjRi4=

n:=20:simplerootser:=series(subs(Q(0,y)=subs(x=0,Qser(n)),Q(0,0)=subs(x=0,y=0,Qser(n)),y=Yser, J1y),t,16)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS5zaW1wbGVyb290c2VyR0YoKzNJInRHRigiIiUiIiIiIzciIiQiIyUpIiImIiRzKCIiKCIlTyIpIiIqIiZLSioiIzYiKF9uNyIiIzgtSSJPR0YlNiNGMSIjOjcjRi4=

Another root comes from I(X)=0 numer(op(1,Ix)/2)

LCoqKiIiJCIiIilJInRHNiIiIiNGJS1JIlVHRig2JEkieEdGKCIiIUYlKUYtRilGJUYlKiZGJ0YlRi9GJUYlRidGJUYtISIi

n:=20: Xser:=op(algeqtoseries(convert(subs(U(x,0)=subs(y=0,User(n)), %%),polynom),t,x,18,true))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVYc2VyR0YoKzdJInRHRigiIiJGMEYwIiIkIiInIiImIiNcIiIoIiR5JSIiKiIlIz0mIiM2IiZDLSciIzgiJyIzTigiIzoiKF1SSSoiIzwtSSJPR0YlNiNGMCIjPjcjRi4=

doublerootser:=series(subs(Q(x,0)=subs(y=0,Qser(n)), x=Xser, I1x),t,18);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS5kb3VibGVyb290c2VyR0YoKzVJInRHRigiIiIhIiIhIiMiIiQhIz8iIiYhJDsjIiIoISUvRCIiKiEmZTAkIiM2IScpRyhRIiM4ISg5OjAmIiM6LUkiT0dGJTYjRjAiIzw3I0Yu

This cannot vanish when x =O(t) diff(I1x,x)

LCYqJkkidEc2IiIiIi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjRiY2I0kiUUdGJTYkSSJ4R0YlIiIhRiZGJiokKUYyIiIjISIiRjc=

We still need to express the double root in terms of the known series Q factor(series(subs(I1=I1x,Ixform),x,3))

KytJInhHNiIsJCooIyIiJSIiKiIiIiwqKihGKEYqKUkidEdGJCIiI0YqLUkiUUdGJDYkIiIhRjNGKiEiIiooRi9GKkkjQjBHRiRGKkYuRipGKiomSSNCMUdGJEYqRi5GKkYqRi9GNEYqRi5GNEYqISIkLCQqKEYnRiosNCooIiInRiopRi5GKEYqKUYwRi9GKkYqKipGPkYqRjZGKkYwRiopRi4iIiRGKkY0KipGQ0YqRjhGKkYwRipGQkYqRjQqJilGNkYvRipGLUYqRioqKkYvRipGNkYqRjhGKkYtRipGKiooRj5GKkZCRiotSSJVR0YkRjJGKkY0KihGKEYqRkJGKi0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRio2I0YxRjJGKkYqKiZGL0YqRi1GKkY0RipGNEYqRi1GNEY0ISIjLCQqKEYnRiosPCooRihGKilGMEZDRipGP0YqRjQqKkY+RipGNkYqRkBGKkZCRipGKioqRkNGKkY4RipGQEYqRkJGKkYqKipGL0YqRkZGKkYwRipGLUYqRjQqLEYoRipGNkYqRjhGKkYwRipGLUYqRjQqKiIjN0YqRkJGKkYwRipGTEYqRjQqKEZGRipGOEYqRi5GKkYqKipGPkYqRjZGKkZMRipGLUYqRioqKkZDRipGOEYqRkxGKkYtRipGKiooRj5GKkYtRiotLUZONiNGSkYyRipGKiooRi9GKkYtRiotLSZGTzYkRipGKkZURjJGKkY0KihGPkYqRi5GKkZJRipGNEYvRjRGKkYuRjRGKkY0LUkiT0dGUEZTRjM=

eqs:=[coeff(%,x,-3), coeff(%,x,-2)]

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcXNHRig3JCwkKigjIiIlIiIqIiIiLCoqKEYyRjQpSSJ0R0YoIiIjRjQtSSJRR0YoNiQiIiFGPUY0ISIiKihGOUY0SSNCMEdGKEY0RjhGNEY0KiZJI0IxR0YoRjRGOEY0RjRGOUY+RjRGOEY+RjQsJCooRjFGNCw0KigiIidGNClGOEYyRjQpRjpGOUY0RjQqKkZHRjRGQEY0RjpGNClGOCIiJEY0Rj4qKkZMRjRGQkY0RjpGNEZLRjRGPiomKUZARjlGNEY3RjRGNCoqRjlGNEZARjRGQkY0RjdGNEY0KihGR0Y0RktGNC1JIlVHRihGPEY0Rj4qKEYyRjRGS0Y0LS0mSSJER0YlNiNGNDYjRjtGPEY0RjQqJkY5RjRGN0Y0Rj5GNEY+RjRGN0Y+Rj43I0Yu

expand(solve(eqs[1],B0))

LCgqKCIiIyIiIkkidEc2IkYlLUkiUUdGJzYkIiIhRitGJUYlKiYjRiVGJEYlSSNCMUdGJ0YlISIiKiRGJkYvRiU=

let us check n:=15: factor(series(subs(U(x,0)=subs(y=0,User(n)),I1=I1x, Q(x,0)=subs(y=0,Qser(n)), B0=doublerootser, B1=simplerootser,Ixform),t,n))

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=

n:=16:factor(series(subs(DD(y)=Dser(n),J1=J1y, Q(0,y)=subs(x=0,Qser(n)),Q(0,0)=subs(x=0,y=0,Qser(n)), B0=doublerootser, B1=simplerootser,Jyform),t,n))

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzc=

We use known results for Gessel's walks in the quadrant

t2T:=(T-1)*(T+3)^3/256/T^3;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR0MlRHRigsJCoqIyIiIiIkYyNGMSwmSSJUR0YoRjFGMSEiIkYxKSwmRjRGMSIiJEYxRjhGMSlGNEY4RjVGMTcjRi4=

with(gfun): Tser:= proc(n) 1+t*op(1,algeqtoseries(subs(T=1+t*P,numer(t^2-t2T)),t,P,n,true)): end: Tser(5); Tser(6)

LCYiIiJGIyomSSJ0RzYiRiMrK0YlIiIlRiMiI08iIiQiJCdSIiImLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjRiMiIidGI0Yj

LCYiIiJGIyomSSJ0RzYiRiMrK0YlIiIlRiMiI08iIiQiJCdSIiImLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjRiMiIihGI0Yj

algTs:=numer(s-t2T)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdUc0dGKCwsKiQpSSJUR0YoIiIlIiIiISIiKigiJGMjRjMpRjEiIiRGM0kic0dGKEYzRjMqJiIiKUYzRjdGM0Y0KiYiIz1GMylGMSIiI0YzRjQiI0ZGMzcjRi4=

Introduce Z=sqrt(T) t2Z:=factor(subs(T=Z^2,t2T));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR0MlpHRigsJCosIyIiIiIkYyNGMSwmSSJaR0YoRjFGMSEiIkYxLCZGNEYxRjFGMUYxKSwmKiQpRjQiIiNGMUYxIiIkRjFGPEYxKUY0IiInRjVGMTcjRi4=

Zser:=proc(n) series(sqrt(Tser(n)),t,n+1): end : Zser(5); Zser(6)

KytJInRHNiIiIiIiIiEiIiNGJyIjOyIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIn

Ky1JInRHNiIiIiIiIiEiIiNGJyIjOyIiJSIkbSIiIictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKQ==

x in terms of T and an additional series U xTU:=factor(solve(16*T^2*(U^2-T)-x*(-2*T+U+U*T)*(-9*T+U^2+8*T*U+T^2-T*U^2),x));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR4VFVHRigsJCosIiM7IiIiKUkiVEdGKCIiI0YxLCYqJClJIlVHRihGNEYxISIiRjNGMUYxLCgqJkYzRjFGOEYxRjEqJkY0RjFGM0YxRjlGOEYxRjksLComRjNGMUY3RjFGOSokRjJGMUYxKigiIilGMUYzRjFGOEYxRjFGNkYxKiYiIipGMUYzRjFGOUY5Rjk3I0Yu

xZU:=factor(subs(T=Z^2,xTU));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR4WlVHRigsJCowIiM7IiIiKUkiWkdGKCIiJUYxLCZJIlVHRihGMUYzISIiRjEsJkY2RjFGM0YxRjEsKComRjZGMSlGMyIiI0YxRjEqJkY8RjFGO0YxRjdGNkYxRjcsKiomRjZGMUYzRjFGMSokRjtGMUYxRjZGMSomIiIkRjFGM0YxRjdGNywqRj9GMUZARjdGNkY3RkFGN0Y3Rjc3I0Yu

The expression of Q(xt,0) QxtZU:= 16*Z^2*(U*Z^2-2*Z^2+U)*(U^3*Z^4+U^2*Z^5-U*Z^6-Z^7-16*U^2*Z^4-16*U*Z^5-2*U^3*Z^2-2*U^2*Z^3+82*U*Z^4+18*Z^5+16*U^2*Z^2+16*U*Z^3-128*Z^4+U^3+U^2*Z-17*U*Z^2-81*Z^3)/((Z-1)*(Z+1)*(Z^2+3)^3*(U*Z+Z^2+U-3*Z)*(U+Z)*(U*Z-Z^2-U-3*Z))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZReHRaVUdGKCwkKjYiIzsiIiIpSSJaR0YoIiIjRjEsKComSSJVR0YoRjFGMkYxRjEqJkY0RjFGMkYxISIiRjdGMUYxLEQqJilGNyIiJEYxKUYzIiIlRjFGMSomKUY3RjRGMSlGMyIiJkYxRjEqJkY3RjEpRjMiIidGMUY5KiQpRjMiIihGMUY5KihGMEYxRkFGMUY+RjFGOSooRjBGMUY3RjFGQkYxRjkqKEY0RjFGPEYxRjJGMUY5KihGNEYxRkFGMSlGM0Y9RjFGOSooIiMjKUYxRjdGMUY+RjFGMSomIiM9RjFGQkYxRjEqKEYwRjFGQUYxRjJGMUYxKihGMEYxRjdGMUZORjFGMSomIiRHIkYxRj5GMUY5KiRGPEYxRjEqJkZBRjFGM0YxRjEqKCIjPEYxRjdGMUYyRjFGOSomIiMiKUYxRk5GMUY5RjEsJkYzRjFGMUY5RjksJkYzRjFGMUYxRjkpLCYqJEYyRjFGMUY9RjFGPUY5LCoqJkY3RjFGM0YxRjFGW29GMUY3RjEqJkY9RjFGM0YxRjlGOSwmRjdGMUYzRjFGOSwqRl1vRjFGW29GOUY3RjlGXm9GOUY5RjE3I0Yu

The correct value of U is the one with CT equal to 1 UserTm1:=proc(n) 1+Tm1*op(1,map(factor,map(allvalues,algeqtoseries(subs(T=1+Tm1,U=1+Tm1*P,numer(x-xTU)),Tm1,P,n+1,true)))): end: UserTm1(4); UserTm1(3)

LCYiIiJGIyomSSRUbTFHNiJGIysvRiUjRiMiIiMiIiEjISIiIiIpRiMsJiomI0YjIiNLRiNJInhHRiZGI0YjI0YjIiM7RiNGKSwoKiYjIiIoIiRHIkYjRjJGI0YsIyIiJkY5RiwqJiNGI0Y5RiMpRjJGKUYjRiMiIiQsKiomIyIjUCIkNyZGI0YyRiNGIyNGOCIkYyNGIyomIyIjNkZERiNGPkYjRiwqJiNGI0ZERiMpRjJGP0YjRiMiIiUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGI0Y7RiNGIw==

LCYiIiJGIyomSSRUbTFHNiJGIystRiUjRiMiIiMiIiEjISIiIiIpRiMsJiomI0YjIiNLRiNJInhHRiZGI0YjI0YjIiM7RiNGKSwoKiYjIiIoIiRHIkYjRjJGI0YsIyIiJkY5RiwqJiNGI0Y5RiMpRjJGKUYjRiMiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGIyIiJUYjRiM=

User:=proc(n) series(subs(Tm1=Tser(n)-1,UserTm1(n)),t,n+1): end: User(6);User(8)

Ky1JInRHNiIiIiIiIiEiIiNGJyIjOyIiJSwmIiRtIkYlKiZGJ0YlSSJ4R0YkRiVGJSIiJy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIp

Ky9JInRHNiIiIiIiIiEiIiNGJyIjOyIiJSwmIiRtIkYlKiZGJ0YlSSJ4R0YkRiVGJSIiJywoKiZGJ0YlKUYtRidGJUYlKiYiI1NGJUYtRiVGJSIlTT5GJSIiKS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiM1

We now consider Q(0,y) yTV:=(1-T+3*V+V*T)/V^2/(3+V+T-V*T);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR5VFZHRigqKCwqKiZJIlRHRigiIiJJIlZHRihGMkYyRjEhIiIqJiIiJEYyRjNGMkYyRjJGMkYyKUYzIiIjRjQsKkYwRjRGMUYyRjNGMkY2RjJGNDcjRi4=

yZV:=factor(subs(T=Z^2,yTV));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR5WlZHRigsJCooLCoqJkkiVkdGKCIiIilJIlpHRigiIiNGM0YzKiRGNEYzISIiKiYiIiRGM0YyRjNGM0YzRjNGMylGMkY2RjgsKkYxRjNGN0Y4RjJGOEY6RjhGOEY4NyNGLg==

QyZV := -16*V*Z^3*(V*Z^2-Z^2-V-3)*(V^3*Z^4-2*V^3*Z^3+V^2*Z^4+4*V^3*Z^2+2*V^2*Z^3+V*Z^4-6*V^3*Z-8*V^2*Z^2-2*V*Z^3+Z^4+3*V^3-2*V^2*Z-8*V*Z^2+2*Z^3+7*V^2+2*V*Z+4*Z^2+7*V+6*Z+3)/((V*Z-V-Z-1)^2*(V+1)^2*(Z^2+3)^3*(Z+1)*(Z-1))

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

the correct V is V = O(t) algeqtoseries(subs(T=1+Tm1,V=Tm1*W,numer(yTV-y)),Tm1,W,3,true)

NyMrK0kkVG0xRzYiIyIiIiIiJSIiISwmKiYjIiIiIiM7IiIiSSJ5RzYiIiIiIiIiIyIiIiIjOyEiIiIiIiwoKiYjIiIiIiNLIiIiKUkieUc2IiIiIyIiIiIiIiomIyIiIiIjSyIiIkkieUc2IiIiIiEiIiMiIiIiI2siIiIiIiMtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMiIiIiIiQ=

VserTm1:=proc(n) Tm1*op(algeqtoseries(subs(T=1+Tm1,V=Tm1*W,numer(yTV-y)),Tm1,W,n,true)): end: VserTm1(4)

KiZJJFRtMUc2IiIiIistRiMjRiUiIiUiIiEsJiomI0YlIiM7RiVJInlHRiRGJUYlRiwhIiJGJSwoKiYjRiUiI0tGJSlGLiIiI0YlRiUqJkYyRiVGLkYlRi8jRiUiI2tGJUY1LCoqJiNGJSIkRyJGJUYuRiVGJSomIyIiJEY8RiVGNEYlRi8qJiMiIiYiJGMjRiUpRi5GP0YlRiUjRiVGQ0YvRj8tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJUYoRiU=

Vser:=proc(n) series(subs(Tm1=Tser(n)-1,VserTm1(n)),t,n+1): end: Vser(6);Vser(8)

KytJInRHNiIiIiIiIiMsJkkieUdGJEYlIiIpRiUiIiUsKComRiZGJSlGKEYmRiVGJSomIiM7RiVGKEYlRiUiIyMpRiUiIictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJUYp

Ky1JInRHNiIiIiIiIiMsJkkieUdGJEYlIiIpRiUiIiUsKComRiZGJSlGKEYmRiVGJSomIiM7RiVGKEYlRiUiIyMpRiUiIicsKiomIiImRiUpRigiIiRGJUYlKiYiI1tGJUYtRiVGJSomIiRGI0YlRihGJUYlIiRXKkYlRiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNQ==

Let us check User(10); Zser(10)

KzFJInRHNiIiIiIiIiEiIiNGJyIjOyIiJSwmIiRtIkYlKiZGJ0YlSSJ4R0YkRiVGJSIiJywoKiZGJ0YlKUYtRidGJUYlKiYiI1NGJUYtRiVGJSIlTT5GJSIiKSwqKiZGJ0YlKUYtIiIkRiVGJSomIiNdRiVGMUYlRiUqJiIkXSdGJUYtRiVGJSImd1MjRiUiIzUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNw==

KzFJInRHNiIiIiIiIiEiIiNGJyIjOyIiJSIkbSIiIiciJU0+IiIpIiZ3UyMiIzUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNw==

n:=12: normal(series(subs(U=User(n), Z=Zser(n), QxtZU),t,1+n))

Ky9JInRHNiIiIiIiIiEsJkkieEdGJEYlIiIjRiVGKSwoKiQpRihGKUYlRiUqJiIiJkYlRihGJUYlIiM2RiUiIiUsKiokKUYoIiIkRiVGJSomIiIqRiVGLEYlRiUqJiIjUEYlRihGJUYlIiMmKUYlIiInLCwqJClGKEYwRiVGJSomIiM5RiVGM0YlRiUqJiIjKClGJUYsRiVGJSomIiRLJEYlRihGJUYlIiQjeUYlIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIzU=

series(subs(y=0,x=t*x,Qser(10)),t,10)

Ky9JInRHNiIiIiIiIiEsJkkieEdGJEYlIiIjRiVGKSwoKiQpRihGKUYlRiUqJiIiJkYlRihGJUYlIiM2RiUiIiUsKiokKUYoIiIkRiVGJSomIiIqRiVGLEYlRiUqJiIjUEYlRihGJUYlIiMmKUYlIiInLCwqJClGKEYwRiVGJSomIiM5RiVGM0YlRiUqJiIjKClGJUYsRiVGJSomIiRLJEYlRihGJUYlIiQjeUYlIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIzU=

Now for Q(0,y) n:=10:normal(series(subs(V=Vser(n),Z=Zser(n),QyZV),t,n+1))

Ky9JInRHNiIiIiIiIiEsJkkieUdGJEYlIiIjRiVGKSwoKiZGKUYlKUYoRilGJUYlKiYiIilGJUYoRiVGJSIjNkYlIiIlLCoqJiIiJkYlKUYoIiIkRiVGJSomIiNJRiVGLEYlRiUqJiIjdEYlRihGJUYlIiMmKUYlIiInLCwqJiIjOUYlKUYoRjBGJUYlKiYiJDciRiVGNEYlRiUqJiIkKFFGJUYsRiVGJSomIiRSKEYlRihGJUYlIiQjeUYlRi4tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNQ==

series(subs(x=0,Qser(n)),t,10)

Ky9JInRHNiIiIiIiIiEsJkkieUdGJEYlIiIjRiVGKSwoKiZGKUYlKUYoRilGJUYlKiYiIilGJUYoRiVGJSIjNkYlIiIlLCoqJiIiJkYlKUYoIiIkRiVGJSomIiNJRiVGLEYlRiUqJiIjdEYlRihGJUYlIiMmKUYlIiInLCwqJiIjOUYlKUYoRjBGJUYlKiYiJDciRiVGNEYlRiUqJiIkKFFGJUYsRiVGJSomIiRSKEYlRihGJUYlIiQjeUYlRi4tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNQ==

Delta; J1y

LCYiIiJGIyoqIiIlRiMpSSJ0RzYiIiIjRiMsJkYjRiNJInlHRihGI0YjLCYqJEYrISIiRiNGI0YjRiNGLg==

LCgqKEkidEc2IiIiIiwmRiZGJkkieUdGJUYmRiYtSSJRR0YlNiQiIiFGKEYmISIiKihGKEYmRiRGLUYnRi1GJiomRiRGJi1GKjYkRixGLEYmRiY=

What is J1(Y)? Let us first express J1y/t in terms of Z and V The value of V when y=0 Vy0:=solve(numer(yTV),V)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRWeTBHRigqJiwmSSJUR0YoIiIiRjEhIiJGMSwmRjBGMSIiJEYxRjI3I0Yu

Q00Z:=factor(subs(V=Vy0,T=Z^2,QyZV))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVRMDBaR0YoLCQqLCIjSyIiIilJIlpHRigiIiRGMSwqKiRGMkYxRjEqJkY0RjEpRjMiIiNGMSEiIiomRjRGMUYzRjFGMUY0RjFGMSwmRjNGMUYxRjFGOiksJiokRjhGMUYxRjRGMUY0RjpGMTcjRi4=

The expression of J1 is simpler than that of Q(0,y) J1overtZV:=factor(subs(Q(0,y)=QyZV,Q(0,0)=Q00Z,y=yZV,T=Z^2,t=sqrt(t2Z), J1y/t))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpKMW92ZXJ0WlZHRigsJCo0IiM7IiIiKSwmSSJWR0YoRjFGMUYxIiIjRjEsKiomRjRGMSlJIlpHRihGNUYxRjEqJEY4RjEhIiIqJiIiJEYxRjRGMUYxRjFGMUYxLCpGN0YxRjpGO0Y0RjtGPUY7RjEpRjlGPUYxKSwmRjpGMUY9RjFGPUY7LCoqJkY0RjFGOUYxRjFGNEYxRjlGO0YxRjFGOywqRkNGMUY0RjtGOUY7RjFGO0Y7RjRGO0YxNyNGLg==

factor(expand(subs(Z=sqrt(T),numer(%))))

LCQqLCIjOyIiIiksJkkiVkc2IkYlRiVGJSIiI0YlLCoqJkkiVEdGKUYlRihGJUYlRi0hIiIqJiIiJEYlRihGJUYlRiVGJUYlLCpGLEYlRi1GLkYoRi5GMEYuRiUpRi0jRjBGKkYlRiU=

factor(expand(subs(Z=sqrt(T),denom(%%))))

KihJIlZHNiIiIiIpLCZJIlRHRiRGJSIiJEYlRilGJSwuKiZGKEYlKUYjIiIjRiVGJSooRi1GJUYoRiVGI0YlISIiKiRGLEYlRi9GKEYlKiZGLUYlRiNGJUYvRiVGL0Yl

J1overtTV:=%%/%

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpKMW92ZXJ0VFZHRigsJCoyIiM7IiIiKSwmSSJWR0YoRjFGMUYxIiIjRjEsKiomSSJUR0YoRjFGNEYxRjFGOCEiIiomIiIkRjFGNEYxRjFGMUYxRjEsKkY3RjFGOEY5RjRGOUY7RjlGMSlGOCNGO0Y1RjFGNEY5KSwmRjhGMUY7RjFGO0Y5LC4qJkY4RjEpRjRGNUYxRjEqKEY1RjFGOEYxRjRGMUY5KiRGQ0YxRjlGOEYxKiZGNUYxRjRGMUY5RjFGOUY5RjE3I0Yu

algY:=subs(y=Y,numer(Delta))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGdZR0YoLCoqKCIiJSIiIilJIllHRigiIiNGMSlJInRHRihGNEYxISIiKigiIilGMUYzRjFGNUYxRjcqJkYwRjFGNUYxRjdGM0YxNyNGLg==

Yser:=proc(n) op(algeqtoseries(algY,t,Y,n,true)): end: Yser(6)

KytJInRHNiIiIiUiIiMiI0tGJSIkPyQiIictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

algYT:=collect(numer(factor(subs(t=sqrt(t2T),algY))),Y,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdZVEdGKCwoKigpSSJZR0YoIiIjIiIiLCZJIlRHRihGM0YzISIiRjMpLCZGNUYzIiIkRjNGOUYzRjYqJiwqKiZGMkYzKUY1IiIlRjNGNiomIiNbRjMpRjVGOUYzRjMqJiIjT0YzKUY1RjJGM0Y2IiNhRjNGM0YxRjNGMyomRjRGM0Y3RjNGNjcjRi4=

algYZ:=collect(numer(factor(subs(t=sqrt(t2Z),algY))),Y,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdZWkdGKCwoKiopSSJZR0YoIiIjIiIiLCZJIlpHRihGM0YzISIiRjMsJkY1RjNGM0YzRjMpLCYqJClGNUYyRjNGMyIiJEYzRjxGM0Y2KiYsKiomRjJGMylGNSIiKUYzRjYqJiIjW0YzKUY1IiInRjNGMyomIiNPRjMpRjUiIiVGM0Y2IiNhRjNGM0YxRjNGMyooRjRGM0Y3RjNGOEYzRjY3I0Yu

Which V corresponds to Y ? A series that is quadratic over Q(T) res:=factor(resultant(numer(yTV-Y),algYT,Y))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRyZXNHRigsJComLDQqJilJIlRHRigiIiMiIiIpSSJWR0YoRjRGNUY1KihGNEY1RjJGNUY3RjVGNSooRjRGNUYzRjVGNkY1RjUqJEYyRjVGNSooIiM3RjVGM0Y1RjdGNSEiIiomIiIkRjVGNkY1Rj0qJkY0RjVGM0Y1RjUqJiIiJ0Y1RjdGNUY9Rj9GPUY1KSwyRjFGNUY4Rj1GOUY1RjpGNUY+Rj1GQEY1RkFGPUY/Rj1GNEY1Rj03I0Yu

Does not factor by introducing sqrt(T) factor(subs(T=Z^2,%))

LCQqJiw0KiYpSSJWRzYiIiIjIiIiKUkiWkdGKCIiJUYqRioqKEYpRipGJ0YqRitGKkYqKihGKUYqRiZGKilGLEYpRipGKiokRitGKkYqKigiIzdGKkYnRipGMEYqISIiKiYiIiRGKkYmRipGNComRilGKkYwRipGKiomIiInRipGJ0YqRjRGNkY0RiopLDJGJUYqRi5GNEYvRipGMUYqRjVGNEY3RipGOEY0RjZGNEYpRipGNA==

Vser(9)

Ky1JInRHNiIiIiIiIiMsJkkieUdGJEYlIiIpRiUiIiUsKComRiZGJSlGKEYmRiVGJSomIiM7RiVGKEYlRiUiIyMpRiUiIicsKiomIiImRiUpRigiIiRGJUYlKiYiI1tGJUYtRiVGJSomIiRGI0YlRihGJUYlIiRXKkYlRiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNQ==

n:=10: series(normal(series(subs(T=Tser(n),V=convert(Vser(n),polynom), y=convert(Yser(n),polynom),op(2,res)),t,n)),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

n:=10: series(normal(series(subs(T=Tser(n),V=convert(Vser(n),polynom), y=convert(Yser(n),polynom),op(3,res)),t,n)),t,n)

KytJInRHNiIiI2siIiUiJSFHIiIiJyImTzIjIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiM1

The equation satisfied by V(Y) algVYT:=collect(subs(V=VY,op(2,res)),VY,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdhbGdWWVRHRigsKCooLCZJIlRHRigiIiIiIiRGMkYyLCZGMUYyRjIhIiJGMilJI1ZZR0YoIiIjRjJGMiomLCgqJkY4RjIpRjFGOEYyRjIqJiIjN0YyRjFGMkY1IiInRjVGMkY3RjJGMiomRjBGMkY0RjJGMjcjRi4=

algVY:=factor(resultant(algVYT,algTs,T))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdWWUdGKCxAKigiKHMlcDwiIiIpSSNWWUdGKCIiKUYxKUkic0dGKCIiI0YxISIiKigiKXdkOjlGMSlGMyIiKEYxRjVGMUY4KihGMEYxRjtGMUY2RjFGMSooIik7X2FcRjEpRjMiIidGMUY1RjFGOCooIilLLzQqKkYxKUYzIiImRjFGNUYxRjgqKCIpL2pRN0YxRkRGMUY2RjFGMSooIipTSSdRN0YxKUYzIiIlRjFGNUYxRjgqKCIpXzpKR0YxRkpGMUY2RjFGMSooRkNGMSlGMyIiJEYxRjVGMUY4KiZGMEYxRkpGMUY4KihGR0YxRk9GMUY2RjFGMSooRj9GMSlGM0Y3RjFGNUYxRjgqKEY6RjFGM0YxRjVGMUY4KihGMEYxRjNGMUY2RjFGMSomRjBGMUY1RjFGODcjRi4=

Equation for J1(Y)/t: it is a rational function in Z factor(resultant(numer(subs(V=VY,J1overtZV-J1overt)), subs(T=Z^2,algVYT), VY))

LCQqLiIjOyIiIilJIlpHNiIiIiVGJSksJiokKUYnIiIjRiVGJSIiJEYlRi5GJSksJkYnRiVGJSEiIiIiJ0YlKSwmRidGJUYlRiVGM0YlKSwsKiZJKEoxb3ZlcnRHRihGJSlGJ0YzRiVGJSooIiIqRiVGOUYlRiZGJUYlKigiI0ZGJUY5RiVGLUYlRiUqJiIkYyNGJSlGJ0YvRiVGMiomRj5GJUY5RiVGJUYuRiVGJQ==

J1Yovertsol:=factor(op(1,[solve(%, J1overt)]))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSxKMVlvdmVydHNvbEdGKCwkKigiJGMjIiIiKUkiWkdGKCIiJEYxKSwmKiQpRjMiIiNGMUYxRjRGMUY0ISIiRjE3I0Yu

J(Y) has degree 8 factor(resultant(numer(JJ-J1Yovertsol), numer(t^2-t2Z),Z)); collect(%,JJ,factor)

LDgqKCI5JXlJIWZmXT1KPFwhNCIiIiIpSSNKSkc2IiIiKUYlKUkidEdGKCIjN0YlRiUqKCI6Y3k0enMlPltZSiU9NSRGJSlGJyIiJ0YlKUYrIiM1RiVGJSooIjk7TyVccUBebCc+bFE+RiVGL0YlKUYrRilGJUYlKigiO29mMmhNJClHPU5vK1RIRiUpRiciIiVGJUY1RiVGJSooIjpDXS0iMz83JzRoPUttJ0YlRjhGJSlGK0YwRiUhIiIqKCI5R3RxIVFKJCpcekkpWzZGJUY4RiUpRitGOUYlRiUqKCI7byR5NnVFS0sjW1IuJkgqRiUpRiciIiNGJUY8RiVGJSooIjpvanVFMSZwaCJlQiZ5QEYlRkNGJUZARiVGPSooIjlbOzw5JWY1JlFzZGg4RiVGQ0YlKUYrRkRGJUY9KiYiODMnRyFwbDx2UiZIcEFGJUZDRiVGJSI5R3hYL14jR2dqczNqJEY9

LCwiOUd4WC9eI0dnanMzaiQhIiIqKCI5JXlJIWZmXT1KPFwhNCIiIiIpSSNKSkc2IiIiKUYnKUkidEdGKiIjN0YnRicqKiI5O08lXHFAXmwnPmxRPkYnKUYtRitGJywmKiYiIztGJylGLSIiI0YnRidGJ0YnRicpRikiIidGJ0YnKioiOUd0cSFRSiQqXHpJKVs2RicpRi0iIiVGJywoKiYiJGMjRidGO0YnRicqJiIjZUYnRjVGJ0YkRidGJ0YnKUYpRjxGJ0YnKioiODMnRyFwbDx2UiZIcEFGJ0YyRicsKEY+RicqJiIjQUYnRjVGJ0YkRidGJ0YnKUYpRjZGJ0Yn

Let us check n:=10: series(subs(Q(0,0)=subs(x=0,y=0,Qser(n)), Q(0,y)=subs(x=0,Qser(n)), y=convert(Yser(n),polynom),J1y/t),t,n+1)

Ky9JInRHNiIiIiUiIiEiIzciIiMiIyUpRiUiJHMoIiInIiVPIikiIiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

series(subs(Z=Zser(n), J1Yovertsol),t,n+1)

KzFJInRHNiIiIiUiIiEiIzciIiMiIyUpRiUiJHMoIiInIiVPIikiIikiJktKKiIjNS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIkYn

The final bit Bovertsol:=factor(subs(t=sqrt(t2Z),1/t^2+2*Q00Z-J1Yovertsol/2))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpCb3ZlcnRzb2xHRigsJCouIiNrIiIiKUkiWkdGKCIiJEYxLCgqJClGMyIiJUYxRjEqJkY4RjEpRjMiIiNGMUYxRjEhIiJGMSwmRjNGMUYxRjxGPCwmRjNGMUYxRjFGPCksJiokRjpGMUYxRjRGMUY0RjxGMTcjRi4=

Expression of (D(y)+2/t^2/(1+y)^2)^2 expr:=4*t^4/9/y^2/Delta*J1overt*(J1overt-Bovert)^2*(J1overt-J1Yovert)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoLCQqMCMiIiUiIioiIiIpSSJ0R0YoRjFGMylJInlHRigiIiMhIiIsJkYzRjMqKkYxRjMpRjVGOEYzLCZGM0YzRjdGM0YzLCYqJEY3RjlGM0YzRjNGM0Y5RjlJKEoxb3ZlcnRHRihGMyksJkZARjNJJ0JvdmVydEdGKEY5RjhGMywmRkBGM0kpSjFZb3ZlcnRHRihGOUYzRjM3I0Yu

exprVZ:=factor(subs(y=yZV, J1overt=J1overtZV,Bovert=Bovertsol,t=sqrt(t2Z),J1Yovert=J1Yovertsol,expr))

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

This is a square is Q(Z,V). Choose the correct sign now exprroot:=-factor(simplify(sqrt(exprVZ),symbolic))

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

factor(subs(Z=sqrt(T),expand(numer(%))))

LCQqMCIjOyIiIilJIlRHNiIjIiIkIiIjRiVJIlZHRihGJSwmRixGJUYlISIiRiUsJkYsRiVGJUYlRiUsSiomKUYnRipGJSlGLCIiJUYlRiUqKEY0RiVGMkYlKUYsRipGJUYuKiYpRidGK0YlRjNGJUYlKigiIidGJUYyRiUpRixGK0YlRiUqKCIjN0YlRjhGJUY2RiVGLiooIiImRiVGJ0YlRjNGJUYuKihGNEYlRjJGJUYsRiVGLiooIiNRRiVGOEYlRjtGJUYlKihGNEYlRidGJUY2RiVGJSomRipGJUYzRiVGJSokRjJGJUYlKihGPUYlRjhGJUYsRiVGLiooRitGJUYnRiVGO0YlRiUqJkY9RiVGNkYlRiUqJEY4RiVGJSooRjRGJUYnRiVGLEYlRiUqJiIjPUYlRjtGJUYlKiZGP0YlRidGJUYuKiZGPUYlRixGJUYlRipGJUYlKSwqKiZGJ0YlRixGJUYlRidGLkYsRi5GKkYuRitGJUYu

factor(subs(Z=sqrt(T),expand(denom(%%))))

LCQqKiIiJCIiIiksJkkiVEc2IkYlRiRGJUYkRiUsMiomKUYoIiIjRiUpSSJWR0YpRi1GJUYlKihGLUYlRixGJUYvRiUhIiIqKEYtRiVGKEYlRi5GJUYlKiRGLEYlRiUqJkYkRiVGLkYlRjEqJkYtRiVGKEYlRiUqJiIiJ0YlRi9GJUYxRiRGMUYlKSwuKiZGKEYlRi5GJUYlKihGLUYlRihGJUYvRiVGMSokRi5GJUYxRihGJSomRi1GJUYvRiVGMUYlRjFGLUYlRiU=

exprrootTV:=%%/%;

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

factor(subs(T=Z^2,exprrootTV^2)/exprVZ)

IiIi

Let us check n:=16: factor(series(subs(V=Vser(n), T=Tser(n), exprrootTV),t,n+1))

Ky9JInRHNiIsJComIyIiIyIiJCIiIiksJkYqRipJInlHRiRGKkYoISIiRiohIiNGJyIiISwmIyIjNUYpRioqJiMiIiVGKUYqRi1GKkYqRigsKCMiIycpRilGKiomIyIjY0YpRipGLUYqRioqJkY2RiopRi1GKEYqRipGNiwqIyIkJSkpRilGKiomIyIkQyhGKUYqRi1GKkYqKiYiIyEqRipGPkYqRioqJiMiI1NGKUYqKUYtRilGKkYqIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRioiIik=

factor(series(Dser(n)+2/3/t^2/(1+y)^2,t,8))

Ky9JInRHNiIsJComIyIiIyIiJCIiIiksJkYqRipJInlHRiRGKkYoISIiRiohIiNGJyIiISwmIyIjNUYpRioqJiMiIiVGKUYqRi1GKkYqRigsKCMiIycpRilGKiomIyIjY0YpRipGLUYqRioqJkY2RiopRi1GKEYqRipGNiwqIyIkJSkpRilGKiomIyIkQyhGKUYqRi1GKkYqKiYiIyEqRipGPkYqRioqJiMiI1NGKUYqKUYtRilGKkYqIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRioiIik=

Let us check that the degree of D(y) is 24 res1:=factor(resultant(numer(exprroot-S),numer(y-yZV),V)): nops(res1)

IiIm

map(indets, [seq(op(i,res1),i=1..nops(res1))])

Nyc8IjwjSSJaRzYiRiRGJDwlSSJTR0YmRiVJInlHRiY=

nops(op(5,res1))

IiR1Iw==

res2:=factor(resultant(op(5,res1),subs(s=t^2, T=Z^2,algTs),Z)): nops(res2)

IiUuJSk=

indets(res2)

PCVJIlNHNiJJInRHRiRJInlHRiQ=

degree(res2,S)

IiND

We need to express I1(x) I1x

LCYqJkkidEc2IiIiIi1JIlFHRiU2JEkieEdGJSIiIUYmRiYqJEYqISIiRiY=

QxtZU

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

I1xtovertZU:=factor(subs(x=x*t,Q(x*t,0)= QxtZU, t=sqrt(t2Z),x=xZU,I1x/t))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSxJMXh0b3ZlcnRaVUdGKCwkKjYiJUM1IiIiKSwoKiZJIlVHRihGMSlJIlpHRigiIiNGMUYxKiZGOEYxRjZGMSEiIkY1RjFGOEYxKUY3IiImRjEsJkY1RjFGN0Y6RjosJkY3RjFGMUY6RjosJkY3RjFGMUYxRjopLCYqJEY2RjFGMSIiJEYxRkNGOiwqKiZGNUYxRjdGMUYxRkJGMUY1RjEqJkZDRjFGN0YxRjpGOiwmRjVGMUY3RjFGOiwqRkVGMUZCRjpGNUY6RkZGOkY6Rjo3I0Yu

Expression of (Aminus(xt)+...)^2 expr:=x^2/9*t^4*I1xtovert*(I1xtovert-Bovert)^2*(I1xtovert-J1Yovert)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoLCQqLiMiIiIiIipGMSlJInhHRigiIiNGMSlJInRHRigiIiVGMUkqSTF4dG92ZXJ0R0YoRjEpLCZGOUYxSSdCb3ZlcnRHRighIiJGNUYxLCZGOUYxSSlKMVlvdmVydEdGKEY9RjFGMTcjRi4=

exprUZ:=factor(subs(x=xZU, I1xtovert=I1xtovertZU,Bovert=Bovertsol,t=sqrt(t2Z),J1Yovert=J1Yovertsol,expr))

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

indets(%)

PCRJIlVHNiJJIlpHRiQ=

Again, his is a square in Q(Z,U) (choose the correct sign) exprrootZU:=-factor(simplify(sqrt(exprUZ),symbolic))

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

factor(subs(Z=sqrt(T),expand(numer(%))))

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

factor(subs(Z=sqrt(T),expand(denom(%%))))

LCQqLCIiJCIiIiwmSSJURzYiRiVGJSEiIkYlKSwmRidGJUYkRiVGJEYlLCYqJClJIlVHRigiIiNGJUYpRidGJUYlKSwsKiZGJ0YlRi5GJUYpKiQpRidGMEYlRiUqKCIiKUYlRidGJUYvRiVGJUYtRiUqJiIiKkYlRidGJUYpRiRGJUYl

exprrootTU:=%%/%

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

Let us check n:=20: factor(series(subs(U=User(n), T=Tser(n), exprrootTU),t,n+1))

Ky9JInRHNiIsJCooIyIiIiIiJEYoLCZJInhHRiRGKEYoISIiRihGK0YsRiwhIiMsJComRidGKEYrRihGKCIiISwkKihGJ0YoRitGKCwmRilGKEYrRihGKEYoIiIjLCQqKEYnRihGK0YoLCgqJClGK0Y0RihGKComIiImRihGK0YoRigiI0BGKEYoRigiIiUsJCooRidGKEYrRigsKiokKUYrRilGKEYoKiYiIilGKEY5RihGKComIiNWRihGK0YoRigiJCY+RihGKEYoIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGRA==

factor(series(subs(x=1/x, x=x*t,Amser(30))+(x+1/x/t^2-1/t^2)/3,t,7))

Ky9JInRHNiIsJCooIyIiIiIiJEYoLCZJInhHRiRGKEYoISIiRihGK0YsRiwhIiMsJComRidGKEYrRihGKCIiISwkKihGJ0YoRitGKCwmRilGKEYrRihGKEYoIiIjLCQqKEYnRihGK0YoLCgqJClGK0Y0RihGKComIiImRihGK0YoRigiI0BGKEYoRigiIiUsJCooRidGKEYrRigsKiokKUYrRilGKEYoKiYiIilGKEY5RihGKComIiNWRihGK0YoRigiJCY+RihGKEYoIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGRA==

Let us check that the degree of Aminus(x) is 24 res1:=factor(resultant(numer(exprrootZU-S),numer(x-xZU),U)): nops(res1)

IiIm

map(indets, [seq(op(i,res1),i=1..nops(res1))])

Nyc8IjwjSSJaRzYiRiRGJDwlSSJTR0YmRiVJInhHRiY=

nops(op(5,res1))

IiQkPQ==

res2:=factor(resultant(op(5,res1),subs(s=t^2, T=Z^2,algTs),Z)): nops(res2)

IiVvWQ==

indets(res2)

PCVJIlNHNiJJInRHRiRJInhHRiQ=

degree(res2,S)

IiND

We denote s=t^2 with(plots):implicitplot(t2T-s,s=0..1/16,T=0..3)

NiktJSdDVVJWRVNHNiQ3W3E3JCQiIiEhIiIkIjFHcHNuPnMtNSEjOjckJCIyLjEzXVp1Ikc8ISM+JCIyTzY0K0VxLywiISM7NyQkIiNEISIlJCIxJlInZVwyJFIsIiEjOjckJCIxalZ2TjQhWyVSISM9JCIyWzMlKkhgMy8tIiEjOzckJCIiJiEiJCQiMkEnZVdKJlJeLSIhIzs3JCQiMWwxXSdSRjk7JyEjPSQiMmgwemYhb01JNSEjOzckJCIjdiEiJSQiMiRIYEk4JFtqLiIhIzs3JCQiMW9wQ2RRMHkkKSEjPSQiMnMtayp5XUdTNSEjOzckJCIiIiEiIyQiMmp6a140ZHYvIiEjOzckJCIycksqekohbyVmNSEjPSQiMiQpKipbPk5CLTAiISM7NyQkIiREIiEiJSQiMk9FQ3EoZXdlNSEjOzckJCIydSZSKHluSTZHIiEjPSQiMidwUiRcaWgsMSIhIzs3JCQiIzohIiQkIjIydCQpKWVZKCpwNSEjOzckJCIyd2VbUkskei06ISM9JCIxVCo9eiopKjRxNSEjOjckJCIyVkFGIXpNa0M6ISM9JCIyKEdrU18mejUyIiEjOzckJCIyZGRSIT1oaDk8ISM9JCIyJ0cpSEk4KlskMyIhIzs3JCQiJHYiISIlJCIyNm9rUl4rZTMiISM7NyQkIjJgOWE9KkdPRD4hIz0kIjJzLU1BdWJzNCIhIzs3JCQiIiMhIiMkIjJFR003RUpANSIhIzs3JCQiMlhyb2NtNGg4IyEjPSQiMmVBUTlOQTU2IiEjOzckJCIkRCMhIiUkIjJWKVFdMz9ZPTYhIzs3JCQiMldHJFtSayZvTSMhIz0kIjJXVVUxJyopeUM2ISM7NyQkIiNEISIkJCIxJ1t0ZHYjek02ISM6NyQkIjFheUg4S2dkRCEjPCQiMUJtJSlwYmJRNiEjOjckJCIkdiMhIiUkIjJ4M1ZJXUI2OiIhIzs3JCQiMk9VN3IpKlwkb0YhIz0kIjI7IzMwekBLXzYhIzs3JCQiMmxTUkVIcG8nRyEjPSQiMXQocFh2ZChlNiEjOjckJCIyeUF0YjZCPyhIISM9JCIxZFdHMSdwJm82ISM6NyQkIiIkISIjJCIyal9uYzYhPXI2ISM7NyQkIjFOMyR5aCdbcEohIzwkIjJPXWsqR1sqcD0iISM7NyQkIiREJCEiJSQiMlYyP0tcMlg+IiEjOzckJCIyRFcpMz8sJnBPJCEjPSQiMGJXOzA/YT8iISM5NyQkIiNOISIkJCIyQmlzMihbJHlAIiEjOzckJCIxXGdNQU9Ua04hIzwkIjJrZkNWRlhRQSIhIzs3JCQiJHYkISIlJCIyLjxEJFtBO1Q3ISM7NyQkIjFjT2dDcig9dyQhIzwkIjJHay9xXHFBQyIhIzs3JCQiMkRNaVtXPWwhUSEjPSQiMnI2TG4mZlZZNyEjOzckJCIxPCNbcDJGdCVSISM8JCIyOGY7Yi00XEUiISM7NyQkIiIlISIjJCIyJDNPMUkkPj1GIiEjOzckJCIxTlhAPHhFSFQhIzwkIjFUUnM5JHkoKUciISM6NyQkIiREJSEiJSQiMmgoUVc3dmgvOCEjOzckJCIyViYzW2QkMzdKJSEjPSQiMjRISlJnWkVKIiEjOzckJCIxJVFiJ2ZXJFtaJSEjPCQiMjhZJyopZVQ2TTghIzs3JCQiMSwnUmdGKFIiXCUhIzwkIjJGb3lWQ0pyTCIhIzs3JCQiI1ghIiQkIjFHYTA9JClwUTghIzo3JCQiMTlGWkdmJGZsJSEjPCQiMW9eaExPNW44ISM6NyQkIiR2JSEiJSQiMnlfbzVPUVVRIiEjOzckJCIxRWUhNGV1LyNbISM8JCIyUGxeRy13cVIiISM7NyQkIjExP19EI2ZoJlwhIzwkIjJjISlmNU8jekA5ISM7NyQkIjJFQyhHKGZMPClcISM9JCIyMD5mQ2kpPkc5ISM7NyQkIiImISIjJCIyKkd5YHJVeEs5ISM7NyQkIjB1IylmRnF2NyYhIzskIjJoYktNLklaWSIhIzs3JCQiJEQmISIlJCIyKSlwQzQ2KVImXCIhIzs3JCQiMVIjeVkmcFN0XyEjPCQiMj0jZlNXOUUsOiEjOzckJCIxVHBVJlx5aEkmISM8JCIyJlxKQWowWjQ6ISM7NyQkIjFZbGMzVkkvYSEjPCQiMkohPSV6RUtJYSIhIzs3JCQiI2IhIiQkIjJtTlxaIUd3djohIzs3JCQiMjlFQTFicjNgJiEjPSQiMmJGZ3JyQGplIiEjOzckJCIxMSdvOjFGRGMmISM8JCIyTlwnUWwoW3JmIiEjOzckJCIyTnktLCIqXEprJiEjPSQiMkBAPjBZQVlqIiEjOzckJCIyJyoqKioqKioqKioqKlxkISM9JCIxJTQ7NGsnRyVvIiEjOjckJCIyJWVsZ2VEbV1kISM9JCIxTSt3KmYlZiVvIiEjOjckJCIwRS9uW2k2diYhIzskIjJ4JClcdidwI1tvIiEjOzckJCIxW0tQaiJSLCVlISM8JCIyWClvYjVBKjN1IiEjOzckJCIyTyYqMyxkNC4qZSEjPSQiMSM9OChwXl1zPCEjOjckJCIyRTdgQ3VSQSNmISM9JCIydDBSISlvdygqeiIhIzs3JCQiMS83PiJSbEgqZiEjPCQiMmlfdz1QJD1nPSEjOzckJCIwLzcyNSlmJSpmISM7JCIyJXB5OSgpeTJpPSEjOzckJCIiJyEiIyQiMjpcak4pZk1vPSEjOzckJCIxem56d0FpX2chIzwkIjJsdFl2RTElSD4hIzs3JCQiMSNIRyQ9c19vZyEjPCQiMi8oKVJTZGh5JT4hIzs3JCQiMVVwbnEqPjk1JyEjPCQiMjljTE1ccSoqKj4hIzs3JCQiMiUqKSlwZFJzUTcnISM9JCIyWUAuaXhSYi4jISM7NyQkIjFGJzQhNCxOVGghIzwkIjFKQmolb1dPMiMhIzo3JCQiMSg0TnIxKTNraCEjPCQiMiRlbE95ekBCQCEjOzckJCIyOnQ8VDUnKUg8JyEjPSQiMnV3JzRReEFdQCEjOzckJCIyJTRaI1xlc0g+JyEjPSQiMkUhKkgwPScqM0AjISM7NyQkIjFZXSZ6VXhzPichIzwkIjE9NyY9bSdRSEEhIzo3JCQiMiZHVVQpSCZROGkhIz0kIjJvQyRwI1F1JilIIyEjOzckJCIydyJHJj5EVGBAJyEjPSQiMk9HbCZcJ0gySiMhIzs3JCQiMWsuSmJSXEZpISM8JCIxImZjW2VfaVEjISM6NyQkIjInR3VzaFZKR2khIz0kIjJkZ2lmLGVRUiMhIzs3JCQiMUVGcSw+JnBCJyEjPCQiMU4qPnF5SVJaIyEjOjckJCIxTFktRjlFUGkhIzwkIjFpanNuJClSeUMhIzo3JCQiMV9lIipway1WaSEjPCQiMiV6Sz0qKSozO2MjISM7NyQkIjJrYDtmRUZKQychIz0kIjIoPW8wWCQ+U2MjISM7NyQkIjJFSnJ1KUhwWWkhIz0kIjFCbU0iPihHXEUhIzo3JCQiMk14aTFRPm5DJyEjPSQiMS8mb2x1UC9sIyEjOjckJCIxMUAoUUcvKFtpISM8JCIydScqNE5SbHB0IyEjOzckJCIyVitiJkciNChbaSEjPSQiMkMwZyc9Ij11dCMhIzs3JCQiMUxwMlVEa1xpISM8JCIyO0p0Y2ZWWSNHISM7NyQkIjEpKmYpSCpIa1xpISM8JCIxLGZnLSlvWiNHISM6NyQkIjE5UF8pSGUqXGkhIzwkIjFjbSR5ekBCIkghIzo3JCQiMTEneWFJZSpcaSEjPCQiMidmJFIxVU9CIkghIzs3JCQiMicpKioqKioqKioqKipcaSEjPSQiI0khIiItJSZDT0xPUkc2JiUkUkdCRyQiKUMpZXElISIpJCIiISEiIiQiKCc+IVwmISIpLSYlJl9BWElTRzYjIiIiNiYtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJiUmX0FYSVNHNiMiIiM2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lK0FYRVNMQUJFTFNHNiQtSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1USJzNiIvJSdmYW1pbHlHUSE2Ii8lJXNpemVHUSMxMDYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSV0cnVlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1EnaXRhbGljNiItSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1USJUNiIvJSdmYW1pbHlHUSE2Ii8lJXNpemVHUSMxMDYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSV0cnVlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1EnaXRhbGljNiItJSlfVklTSUJMRUc2IyIiIi0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJFMnISIiLSUpQk9VTkRTX1lHNiMkIiRTIiEiIi0lLUJPVU5EU19XSURUSEc2IyQiJSFHJCEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiU/TSEiIi0lKUNISUxEUkVORzYiLSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZRzYjJCIiISEiIi0lLUJPVU5EU19XSURUSEc2IyQiJStTISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJStTISIiLSUpQ0hJTERSRU5HNiI=NiI=

algTs:=numer(t2T-s)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdUc0dGKCwsKiQpSSJUR0YoIiIlIiIiRjMqKCIkYyNGMylGMSIiJEYzSSJzR0YoRjMhIiIqJiIiKUYzRjZGM0YzKiYiIz1GMylGMSIiI0YzRjMiI0ZGOTcjRi4=

factor(discrim(%,T))

LCQqKCItR0QlZkFJJCIiIilJInNHNiIiIiNGJSksJiomIiM7RiVGJ0YlRiVGJSEiIkYpRiVGLg==

map(simplify,map(allvalues,algeqtoseries(subs(s=1/16*(1-epsilon),algTs),epsilon,T,10))): Tsing:=op(3,%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZUc2luZ0dGKCw4IiIkIiIiKihGL0YwKSIiIyNGM0YvRjApSShlcHNpbG9uR0YoI0YwRi9GMCEiIiooIyIiKkYzRjApRjNGN0YwKUY2RjRGMEYwKiYjIiNAIiIlRjBGNkYwRjgqKCMiI1AiIztGMEYyRjApRjYjRkFGL0YwRjAqKCNGQEZFRjBGPEYwKUY2IyIiJkYvRjBGOComI0YvIiNrRjApRjZGM0YwRjAqKCMiI3oiJCM+RjBGMkYwKUY2IyIiKEYvRjBGMCooIyIkNiMiJDcmRjBGPEYwKUY2IyIiKUYvRjBGOComIyIjTCIlQzVGMClGNkYvRjBGMC1JIk9HRiU2IyokKUY2IyIjNUYvRjBGMDcjRi4=

Zsing:=series(sqrt(Tsing),epsilon,10)

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

xTU

LCQqLCIjOyIiIilJIlRHNiIiIiNGJSwmKiQpSSJVR0YoRilGJSEiIkYnRiVGJSwoKiZGJ0YlRi1GJUYlKiZGKUYlRidGJUYuRi1GJUYuLCwqJkYnRiVGLEYlRi4qJEYmRiVGJSooIiIpRiVGJ0YlRi1GJUYlRitGJSomIiIqRiVGJ0YlRi5GLkYu

User(10)

KzFJInRHNiIiIiIiIiEiIiNGJyIjOyIiJSwmIiRtIkYlKiZGJ0YlSSJ4R0YkRiVGJSIiJywoKiZGJ0YlKUYtRidGJUYlKiYiI1NGJUYtRiVGJSIlTT5GJSIiKSwqKiZGJ0YlKUYtIiIkRiVGJSomIiNdRiVGMUYlRiUqJiIkXSdGJUYtRiVGJSImd1MjRiUiIzUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNw==

algUTx:=collect(numer(x-xTU),U,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdhbGdVVHhHRigsKioqSSJ4R0YoIiIiLCZJIlRHRihGMUYxISIiRjEsJkYzRjFGMUYxRjEpSSJVR0YoIiIkRjFGNCoqIiIjRjFGM0YxLCgqKCIiJkYxRjNGMUYwRjFGMSomIiIpRjFGM0YxRjQqJkY4RjFGMEYxRjFGMSlGN0Y6RjFGMSoqRjNGMUYwRjEsKCokKUYzRjpGMUYxKiYiI0NGMUYzRjFGNCIiKkY0RjFGN0YxRjEqKEY6RjFGRUYxLCgqJkYzRjFGMEYxRjFGPkY0KiZGSEYxRjBGMUY0RjFGNDcjRi4=

UserTm1(5)

LCYiIiJGIyomSSRUbTFHNiJGIysxRiUjRiMiIiMiIiEjISIiIiIpRiMsJiomI0YjIiNLRiNJInhHRiZGI0YjI0YjIiM7RiNGKSwoKiYjIiIoIiRHIkYjRjJGI0YsIyIiJkY5RiwqJiNGI0Y5RiMpRjJGKUYjRiMiIiQsKiomIyIjUCIkNyZGI0YyRiNGIyNGOCIkYyNGIyomIyIjNkZERiNGPkYjRiwqJiNGI0ZERiMpRjJGP0YjRiMiIiUsLCMiI0AiJUM1RiwqJiNGSUY5RiNGMkYjRiwqJiMiIyIpIiVbP0YjRj5GI0YjKiYjRjhGUUYjRkxGI0YsKiYjRiNGV0YjKUYyRk1GI0YjRjstSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNGIyIiJ0YjRiM=

Uxser:=proc(n) op(1,simplify(map(allvalues,algeqtoseries(subs(T=Z^2,algUTx),x,U,n,true)),symbolic)): end: Uxser(5)

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

Q(xt,0) is a series in x with coefficients in Q(Z) Qxtserx:=proc(n) factor(series(subs(U=Uxser(n),QxtZU),x,n+1)): end: Qxtserx(4);

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

n:=20:series(subs(Z=Zser(n), coeff(%%,x,3)/t^3),t,n)

KzNJInRHNiIiIiIiIiQiIzkiIiYiJHMiIiIoIiUnNCMiIioiJkZmIyIjNiInPHBLIiM4IigiZSo+JSIjOi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiM8

coeff(coeff(Qser(17),x,3),y,0)

LDIqJiIpclknWyYiIiIpSSJ0RzYiIiM8RiVGJSomIigiZSo+JUYlKUYnIiM6RiVGJSomIic8cEtGJSlGJyIjOEYlRiUqJiImRmYjRiUpRiciIzZGJUYlKiYiJSc0I0YlKUYnIiIqRiVGJSomIiRzIkYlKUYnIiIoRiVGJSomIiM5RiUpRiciIiZGJUYlKiQpRiciIiRGJUYl

Singular behaviour of U: There occurs a cubic function of x that we call M(x) Using:=map(factor,subs(eta=epsilon^(1/3), RootOf(2*x*_Z^3+(-27*x+36)*_Z^2+54*x*_Z-27*x-108)=M(x), op(algeqtoseries(subs(T=simplify(subs(epsilon=eta^3,convert(Tsing,polynom)),symbolic),algUTx),eta,U,5))))

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

alias(Mexpl=RootOf(2*x*_Z^3+(-27*x+36)*_Z^2+54*x*_Z-27*x-108))

SSZNZXhwbEc2Ig==

algM:=subs(_Z=M,2*x*_Z^3+(-27*x+36)*_Z^2+54*x*_Z-27*x-108)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGdNR0YoLCwqKCIiIyIiIkkieEdGKEYxKUkiTUdGKCIiJEYxRjEqJiwmKiYiI0ZGMUYyRjEhIiIiI09GMUYxKUY0RjBGMUYxKigiI2FGMUYyRjFGNEYxRjFGOEY6IiQzIkY6NyNGLg==

xM:=factor(solve(algM,x))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN4TUdGKCwkKioiI08iIiIsJiokKUkiTUdGKCIiI0YxRjEiIiQhIiJGMSwmKiZGNkYxRjVGMUYxRjdGOEY4LChGM0YxKiYiIzdGMUY1RjFGOCIiKkYxRjhGODcjRi4=

Let us choose the right series M(x): it is the value of U at t=1/4 Msersol:=map(allvalues,algeqtoseries(algM,x,M,3))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShNc2Vyc29sR0YoNyUrK0kieEdGKCEjPSEiIiMiI0YiIiMiIiEjIiImIiIkIiIiLUkiT0dGJTYjRjpGNSsrRjAqJClGOSNGOkY1RjpGNiwmI0Y4IiInRjIqJkZBRjpGQEY6RjpGOiwmIyIjPCIjQ0YyKiYjIiMqKSIkOyNGOkZARjpGOkY1RjtGOSsrRjAsJEY/RjJGNiwmRkNGMkZFRjJGOiwmRkdGMkZKRjJGNUY7Rjk3I0Yu

User(8)

Ky9JInRHNiIiIiIiIiEiIiNGJyIjOyIiJSwmIiRtIkYlKiZGJ0YlSSJ4R0YkRiVGJSIiJywoKiZGJ0YlKUYtRidGJUYlKiYiI1NGJUYtRiVGJSIlTT5GJSIiKS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiM1

Watch out here: we need the series that starts with sqrt 3 Mser:=proc(n) op(1,map(allvalues,algeqtoseries(algM,x,M,n,true))): end: Mser(5)

Ky9JInhHNiIqJCkiIiQjIiIiIiIjRikiIiEsJiMiIiYiIichIiIqJkYoRilGJkYpRilGKSwmIyIjPCIjQ0YwKiYjIiMqKSIkOyNGKUYmRilGKUYqLCYjIiVmPCIlI2YjRjAqJiMiJDgiIiQpR0YpRiZGKUYpRicsJiomIyImLEYiIiYvNiRGKUYmRilGKSMiJUp0IiZvLiJGMCIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpRi4=

We can simplify the expansion of U using the expression of x in terms of M Using:=map(factor,subs(M(x)=M,x=xM,Using))

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

Singular behaviour of V algVTy:=numer(y-yTV)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdhbGdWVHlHRigsMiooSSJUR0YoIiIiKUkiVkdGKCIiJEYxSSJ5R0YoRjFGMSooRjBGMSlGMyIiI0YxRjVGMSEiIiomRjJGMUY1RjFGOSooRjRGMUY3RjFGNUYxRjkqJkYwRjFGM0YxRjFGMEY5KiZGNEYxRjNGMUYxRjFGMTcjRi4=

This is where we introduce the series P(y) algeqtoseries(subs(T=simplify(subs(epsilon=eta^3,convert(Tsing,polynom)),symbolic),algVTy),eta,V,2)

NyMrKUkkZXRhRzYiLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKiomKUkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiQiIiJJInlHNiIiIiIiIiIqKCIiJCIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIjIiIiSSJ5RzYiIiIiISIiKiYiIiQiIiJJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiIiIiIiIiISIiIiIhLCQqKiMiIiIiIiMiIiIpIiIjIyIiIyIiJCIiIiwqKiZJInlHNiIiIiIpLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKiomKUkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiQiIiJJInlHNiIiIiIiIiIqKCIiJCIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIjIiIiSSJ5RzYiIiIiISIiKiYiIiQiIiJJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiIiIiIiIiISIiIiIjIiIiIiIiKiZJInlHNiIiIiItSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywqKiYpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIkkieUc2IiIiIiIiIiooIiIkIiIiKUkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiMiIiJJInlHNiIiIiIhIiIqJiIiJCIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIiIiIiIiIhIiIiIiIhIiItSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywqKiYpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIkkieUc2IiIiIiIiIiooIiIkIiIiKUkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiMiIiJJInlHNiIiIiIhIiIqJiIiJCIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIiIiIiIiIhIiIhIiIiIiIiIiIiIiIsJkkieUc2IiIiIiIiIiEiIiEiIiIiIiIiIi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyIiIiIiIw==

Vsing:= map(factor,subs(eta=epsilon^(1/3), RootOf(_Z^3*y-3*_Z^2*y+3*_Z-1)=P(y), op(algeqtoseries(subs(T=simplify(subs(epsilon=eta^3,convert(Tsing,polynom)),symbolic),algVTy),eta,V,5) )))

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

alias(Pexpl=RootOf(_Z^3*y-3*_Z^2*y+3*_Z-1))

NiRJJk1leHBsRzYiSSZQZXhwbEdGJA==

algP:=subs(_Z=P,_Z^3*y-3*_Z^2*y+3*_Z-1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGdQR0YoLCoqJilJIlBHRigiIiQiIiJJInlHRihGM0YzKihGMkYzKUYxIiIjRjNGNEYzISIiKiZGMkYzRjFGM0YzRjNGODcjRi4=

yP:=factor(solve(algP,y))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN5UEdGKCwkKigsJiomIiIkIiIiSSJQR0YoRjNGM0YzISIiRjMpRjQiIiNGNSwmRjRGM0YyRjVGNUY1NyNGLg==

map(allvalues,algeqtoseries(algP,y,P,3))

NyUrK0kieUc2IiMiIiIiIiQiIiEjIiIpIiMiKUYnIyIjUyIkSCgiIiMtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNGJ0YoLCoqKF4jRidGJylGKCNGJ0YwRicpRiRGOyEiIkYnIyIiJUYoRicqKCwkKiYjRj8iIipGJ0Y5RidGJ0YnRjpGJ0Y8RidGPS1GMjYjRiRGJywqKigsJEY5RidGJ0Y6RidGPEY9Rj1GPkYnKihGQkYnRjpGJ0Y8RidGJ0ZFRic=

Choose the correct value of P(y) Vser(4)

KylJInRHNiIiIiIiIiMsJkkieUdGJEYlIiIpRiUiIiUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJw==

Pser:=proc(n) op(algeqtoseries(algP,y,P,n,true)): end: Pser(5)

Ky9JInlHNiIjIiIiIiIkIiIhIyIiKSIjIilGJiMiI1MiJEgoIiIjIyIkRygiJiRvPkYnIyImb1AlIihCVmYiIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiYiIiY=

We can simplify the expansion of V using the expression of y in terms of P Vsing:=map(factor,subs(P(y)=P,y=yP,Vsing))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZWc2luZ0dGKCwuSSJQR0YoIiIiKi4jRjAiIiNGMClGMyNGMyIiJEYwLCZGL0YwRjBGMEYwKUkoZXBzaWxvbkdGKCNGMEY2RjBGL0YwLCZGL0YwRjAhIiJGPEYwKi5GMkYwKUYzRjpGMClGL0YzRjBGN0YwKUY5RjVGMClGO0YzRjxGMCouI0YwIiNDRjBGN0YwLCwqJiIiKkYwKUYvIiIlRjBGMComRklGMClGL0Y2RjBGPComIiNRRjBGP0YwRjwqJiIjP0YwRi9GMEYwRjZGPEYwRjlGMEYvRjApRjsiIiZGPEYwKjAjRjAiIycqRjBGNEYwRjdGMCwwKiYiI0JGMClGLyIiJ0YwRjAqJiIjXUYwKUYvRlFGMEY8KiYiI3ZGMEZIRjBGPComIiRzIkYwRktGMEYwKiYiI1RGMEY/RjBGMComIiNlRjBGL0YwRjwiIzZGMEYwKUY5I0ZJRjZGMEYvRjApRjsiIihGPEYwLUkiT0dGJTYjKiQpRjkjRlFGNkYwRjA3I0Yu

JSFH

ser:=map(factor,series(subs(U=Using,Z=Zsing,QxtZU),epsilon,2));

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

As expected, first singular term in epsilon^(4/3). Note that the factorization does not work well here op(3,ser)

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

But with epsilon=1, Maple is able to factor... c2:=factor(subs(epsilon=1,op(3,ser)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjMkdGKCwkKiwiIiciIiIpIiIkI0YxIiIjRjEpRjUjRjVGM0YxKSwmKiZGNUYxSSJNR0YoRjFGMUYzISIiRjVGMSksJkY7RjFGM0Y8IiIlRjxGMTcjRi4=

evalf(GAMMA(-4/3))

JCIramB3WUkhIio=

We denote L(x)=M(4x) HxquadL:=2^(7/3)*subs(M=L,c2)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShIeHF1YWRMR0YoLCQqKiIjWyIiIikiIiQjRjEiIiNGMSksJiomRjVGMUkiTEdGKEYxRjFGMyEiIkY1RjEpLCZGOUYxRjNGOiIiJUY6RjE3I0Yu

xM

LCQqKiIjTyIiIiwmKiQpSSJNRzYiIiIjRiVGJSIiJCEiIkYlLCYqJkYrRiVGKUYlRiVGLEYtRi0sKEYnRiUqJiIjN0YlRilGJUYtIiIqRiVGLUYt

Lser:=proc(n) subs(x=4*x,Mser(n)): end: Lser(2)

KyksJComIiIlIiIiSSJ4RzYiRiZGJiokKSIiJCNGJiIiI0YmIiIhLCYjIiImIiInISIiKiZGLEYmRipGJkYmRiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YoNiNGJkYt

Hxquadser:=proc(n) map(factor,map(expand,map(rationalize,series(subs(L=Lser(n),HxquadL),x,n+1)))): end: Hxquadser(5)

Ky9JInhHNiIsJComIiIlIiIiKSIiJCNGKCIiI0YoRigiIiEjIiNLRipGKCwmKiYjIiRHIiIjRkYoRilGKCEiIiMiI2tGKkYoRiwsJiMiJXNRIiMiKUYoKiYjIiQ3JkY0RihGKUYoRjVGKiwmKiYjIiZXNCYiJEgoRihGKUYoRjUjIiU3UEY0RihGJy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIm

Let us check N:=100:i:=0: plot([seq([1/n,coeff(coeff(coeff(Qser(N),x,i),y,0),t,n)/4^(n)*n^(7/3)],n=1..N)],abs=0..0.1,ord=1.5..2.5,style=point);

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

evalf(4*sqrt(3)/GAMMA(-4/3))

JCIrYk8mUkYjISIq

N:=100:i:=1: plot([seq([1/n,coeff(coeff(coeff(Qser(N),x,i),y,0),t,n)/4^(n)*n^(7/3)],n=1..N)],abs=0..0.1,ord=2.5..3.7,style=point);

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NiI=

Hxquadser(2)

KylJInhHNiIsJComIiIlIiIiKSIiJCNGKCIiI0YoRigiIiEjIiNLRipGKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRiw=

evalf(coeff(%,x,i)/GAMMA(-4/3))

JCIrejEpNF0kISIq

N:=120:i:=2: plot([seq([1/n,coeff(coeff(coeff(Qser(N),x,i),y,0),t,n)/4^(n)*n^(7/3)],n=1..N)],abs=0..0.02,ord=3.5..4.4,style=point);

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Ig==

Hxquadser(3)

KytJInhHNiIsJComIiIlIiIiKSIiJCNGKCIiI0YoRigiIiEjIiNLRipGKCwmKiYjIiRHIiIjRkYoRilGKCEiIiMiI2tGKkYoRiwtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKEYq

evalf(coeff(%,x,i)/GAMMA(-4/3))

JCIrc14hcEklISIq

ser:=map(factor,series(subs(V=Vsing,Z=Zsing,QyZV),epsilon,2));

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

As expected, first singular term in epsilon^(4/3) (again, some factorizations were not done in the coefficients of ser) c2:=factor(subs(Pexpl=P(y),epsilon=1,op(3,ser)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjMkdGKCwkKjAjIiIlIiIkIiIiKUYyI0YzIiIjRjMpRjYjRjZGMkYzLCZJIlBHRihGM0YyISIiRjMpRjpGMkYzLCZGOkYzRjNGM0Y7KSwmRjpGM0YzRjtGMUY7Rjs3I0Yu

HyquadP:=2^(7/3)*c2

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShIeXF1YWRQR0YoLCQqLiMiI0siIiQiIiIpRjIjRjMiIiNGMywmSSJQR0YoRjNGMiEiIkYzKUY4RjJGMywmRjhGM0YzRjNGOSksJkY4RjNGM0Y5IiIlRjlGOTcjRi4=

Hyquadser:=proc(n) series(subs(P=Pser(n),HyquadP),y,n+1): end

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpIeXF1YWRzZXJHRihmKjYjSSJuR0YoRihGKEYoLUknc2VyaWVzR0YmNiUtSSVzdWJzR0YmNiQvSSJQR0YoLUklUHNlckdGKEYvSShIeXF1YWRQR0YoSSJ5R0YoLCZGMCIiIkY+Rj5GKEYoRig3I0Yu

Hyquadser(4)

Ky1JInlHNiIsJComIiIlIiIiKSIiJCNGKCIiI0YoRigiIiEsJComIyIkWyIiI0ZGKEYpRihGKEYoLCQqJiMiJTNaIiRIKEYoRilGKEYoRiwsJComIyInUz45IiYkbz5GKEYpRihGKEYqLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGJw==

Hyquad has degree 3 factor(resultant(numer(HyquadP/sqrt(3)-S),algP,P))

LDoqKCIlRzwiIiIpSSJTRzYiIiIkRiUpSSJ5R0YoIiImRiVGJSooIiUlPSZGJUYmRiUpRisiIiVGJSEiIiooIiVjTUYlRiZGJSlGK0YpRiVGJSooIiU3cEYlKUYnIiIjRiVGL0YlRjEqKEYzRiVGJkYlKUYrRjhGJUYlKigiJlt3I0YlRjdGJUY0RiVGJSooRi5GJUYmRiVGK0YlRjEqKCImczklRiVGN0YlRjpGJUYxKiZGJEYlRiZGJUYlKihGPEYlRjdGJUYrRiVGJSomRjZGJUY3RiVGMSomIidXQEVGJUYrRiVGMQ==

Let us check N:=100:j:=0: plot([seq([1/n,coeff(coeff(coeff(Qser(N),x,0),y,j),t,n)/4^(n)*n^(7/3)],n=1..N)],abs=0..0.1,ord=1.5..2.5,style=point);

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

evalf(4*sqrt(3)/GAMMA(-4/3))

JCIrYk8mUkYjISIq

N:=100:j:=1: plot([seq([1/n,coeff(coeff(coeff(Qser(N),x,0),y,j),t,n)/4^(n)*n^(7/3)],n=1..N)],abs=0..0.1,ord=2..3.5,style=point);

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Ig==

Hyquadser(2)

KylJInlHNiIsJComIiIlIiIiKSIiJCNGKCIiI0YoRigiIiEsJComIyIkWyIiI0ZGKEYpRihGKEYoLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGLA==

evalf(coeff(%,y,j)/GAMMA(-4/3))

JCIrOChlaDYkISIq

N:=120:j:=2: plot([seq([1/n,coeff(coeff(coeff(Qser(N),x,0),y,j),t,n)/4^(n)*n^(7/3)],n=1..N)],abs=0..0.02,ord=2.5..4,style=point);

NistJSdDVVJWRVNHNiQ3ZHI3JCQiIzUhIiIkIiIhISIiNyQkIiImISIiJCIiISEiIjckJCIrTExMTEwhIzUkIiIhISIiNyQkIiNEISIjJCIrOjhEJSk+ISM1NyQkIiIjISIiJCIiISEiIjckJCIrbm1tbTshIzUkIitSZkIieiUhIzU3JCQiK0g5ZEc5ISM1JCIiISEiIjckJCIkRCIhIiQkIip2JGZldiEiKjckJCIrNjY2NjYhIzUkIiIhISIiNyQkIiIiISIiJCIrTCIzWCsiISIqNyQkIisiNDQ0NCohIzYkIiIhISIiNyQkIitMTExMJCkhIzYkIisqWz48QSIhIio3JCQiKyNwMkJwKCEjNiQiIiEhIiI3JCQiK1ZyJkc5KCEjNiQiK1oyPjU5ISIqNyQkIitubW1tbSEjNiQiIiEhIiI3JCQiJEQnISIlJCIrJTNfUmQiISIqNyQkIjIxKys1JUhOIyllISM9JCIiISEiIjckJCIrY2JiYmIhIzYkIitOQyFwciIhIio3JCQiKyYqeTpqXyEjNiQiIiEhIiI3JCQiIiYhIiMkIis7WVRVPSEiKjckJCIraVohPnclISM2JCIiISEiIjckJCIrWFhYWFghIzYkIitbO0hgPiEiKjckJCIrKDNFeU0lISM2JCIiISEiIjckJCIrbm1tbVQhIzYkIisncEg9MCMhIio3JCQiIiUhIiMkIiIhISIiNyQkIitZUTpZUSEjNiQiKy9OISpSQCEiKjckJCIrL1BxLlAhIzYkIiIhISIiNyQkIityJkc5ZCQhIzYkIismcFkhPkEhIio3JCQiK2llRltNISM2JCIiISEiIjckJCIrTExMTEwhIzYkIislWz4wSCMhIio3JCQiK19rIWVBJCEjNiQiIiEhIiI3JCQiJURKISImJCIrV0xPYkIhIio3JCQiKi4uLi4kISM1JCIiISEiIjckJCIrcms8VEghIzYkIitQVlc5QyEiKjckJCIrZEc5ZEchIzYkIiIhISIiNyQkIit5eHh4RiEjNiQiK1ZzW29DISIqNyQkIisuRnEtRiEjNiQiIiEhIiI3JCQiK1oqeTpqIyEjNiQiKzhDNT1EISIqNyQkIitrRDVrRCEjNiQiIiEhIiI3JCQiI0QhIiQkIitycCFRYyMhIio3JCQiKlJDIVJDISM1JCIiISEiIjckJCIrIlFfNFEjISM2JCIrLzsvMUUhIio3JCQiKyZSImVEQiEjNiQiIiEhIiI3JCQiK3Rzc3NBISM2JCIrWlI9WEUhIio3JCQiK0FBQUFBISM2JCIiISEiIjckJCIrVkkiUjwjISM2JCIrNiRmOm8jISIqNyQkIit1JmZ3NyMhIzYkIiIhISIiNyQkIitMTEwkMyMhIzYkIitHJFxhciMhIio3JCQiK0ZqIjMvIyEjNiQiIiEhIiI3JCQiIiMhIiMkIitpKik0WkYhIio3JCQiKzlWeWc+ISM2JCIiISEiIjckJCIrQnAyQj4hIzYkIitOQXN3RiEiKjckJCIrYEN6Jyk9ISM2JCIiISEiIjckJCIrXz0mPSY9ISM2JCIrQXBdL0chIio3JCQiKz09PT09ISM2JCIiISEiIjckJCIrJ0c5ZHkiISM2JCIrPiU9MSRHISIqNyQkIitsZlFhPCEjNiQiIiEhIiI3JCQiK0p6OEM8ISM2JCIraUg/YkchIio3JCQiK2FfIlxwIiEjNiQiIiEhIiI3JCQiK25tbW07ISM2JCIrMS5SeUchIio3JCQiK2lVTVI7ISM2JCIiISEiIjckJCIrRUshSGgiISM2JCIrcmZIK0ghIio3JCQiKyhlLHRlIiEjNiQiIiEhIiI3JCQiJkRjIiEiJyQiK0dKLUBIISIqNyQkIitROllROiEjNiQiIiEhIiI3JCQiKzo6Ojo6ISM2JCIrMFVtU0ghIio3JCQiKzh0YCNcIiEjNiQiIiEhIiI3JCQiK04jKWVxOSEjNiQiK1FBSWZIISIqNyQkIitpYEZcOSEjNiQiIiEhIiI3JCQiK0g5ZEc5ISM2JCIrTj8seEghIio3JCQiKy8yWDM5ISM2JCIiISEiIjckJCIrKikpKSkpKVEiISM2JCIraDYnUSpIISIqNyQkIis5SScpcDghIzYkIiIhISIiNyQkIiteOE5eOCEjNiQiKyl6NSo0SSEiKjckJCIrTExMTDghIzYkIiIhISIiNyQkIit1JSp5OjghIzYkIit0a0BESSEiKjckJCIrKkgsKClIIiEjNiQiIiEhIiI3JCQiKyNHXj9HIiEjNiQiKypwRylSSSEiKjckJCIrJnlBZUUiISM2JCIiISEiIjckJCIkRCIhIiUkIitDTnpgSSEiKjckJCIrLHpjTTchIzYkIiIhISIiNyQkIismPjcmPjchIzYkIis7STpuSSEiKjckJCIreCM+Wz8iISM2JCIiISEiIjckJCIqPncvPiIhIzUkIit6YyUqekkhIio3JCQiKyllcWs8IiEjNiQiIiEhIiI3JCQiKylwIXppNiEjNiQiK0NvPyM0JCEiKjckJCIrKEdEJVw2ISM2JCIiISEiIjckJCIrT09PTzYhIzYkIiskKilvUjUkISIqNyQkIisxYmZCNiEjNiQiIiEhIiI3JCQiKzY2NjY2ISM2JCIrWDxFOkohIio3JCQiKyo0LCopNCIhIzYkIiIhISIiNyQkIitBbCZwMyIhIzYkIissSDZFSiEiKjckJCIrPClvXzIiISM2JCIiISEiIjckJCIrKHlIUTEiISM2JCIqeVpsOCQhIik3JCQiK3o6al81ISM2JCIiISEiIjckJCIrbm1tVDUhIzYkIiskKSkqZVlKISIqNyQkIitOeSM0LiIhIzYkIiIhISIiNyQkIitqIjMvLSIhIzYkIisiKTRFY0ohIio3JCQiKiwsLCwiISM1JCIiISEiIjckJCIiIiEiIyQiK2k3ZWxKISIqNyQkIisqNCEqNCEqKiEjNyQiIiEhIiI3JCQiK3A6I1IhKSohIzckIit4JXBYPCQhIio3JCQiK2t5dDMoKiEjNyQiIiEhIiI3JCQiKzpZUTonKiEjNyQiK3BJQyQ9JCEiKjckJCIrQyY0UV8qISM3JCIiISEiIjckJCIra0EnUlYqISM3JCIreCM9Oz4kISIqNyQkIiskUiV6WCQqISM3JCIiISEiIjckJCIrZiNmI2YjKiEjNyQiK1Ytcio+JCEiKjckJCIrRj5KdSIqISM3JCIiISEiIjckJCIrIjQ0NDQqISM3JCIrLUpgMkshIio3JCQiKzQhNCE0ISohIzckIiIhISIiNyQkIitIOWRHKikhIzckIitrKzU6SyEiKjckJCIrQXZiXCkpISM3JCIiISEiIjckJCIrRClIPngpISM3JCIrKVtCQ0EkISIqNyQkIit1QGwmcCkhIzckIiIhISIiNyQkIitiJypvPycpISM3JCIrXlxeSEshIio3JCQiK1omM3FhKSEjNyQiIiEhIiI3JCQiK3JpZHUlKSEjNyQiKzNgUU9LISIqNyQkIjEqKioqKlxNaExTKSEjPSQiIiEhIiI3JCQiMSwrK0xMTEwkKSEjPSQiK1paL1ZLISIqLSUmQ09MT1JHNiclJFJHQkckIilDKWVxJSEiKSQiIiEhIiIkIignPiFcJiEiKS0lK19BVFRSSUJVVEVHNiMvJSdzb3VyY2VHJSxtYXRoZGVmYXVsdEctJSVWSUVXRzYkOyQiIiEhIiIkIiIjISIjOyQiI0QhIiIkIiNTISIiLSYlJl9BWElTRzYjIiIiNiYtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJiUmX0FYSVNHNiMiIiM2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lK0FYRVNMQUJFTFNHNiQtSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1USRhYnM2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiItSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1USRvcmQ2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2Ii0lJlNUWUxFRzYjJSZQT0lOVEctJSlfVklTSUJMRUc2IyIiIi0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJFMoISIiLSUpQk9VTkRTX1lHNiMkIiRTIiEiIi0lLUJPVU5EU19XSURUSEc2IyQiJStJISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJT9NISIiLSUpQ0hJTERSRU5HNiItJStBTk5PVEFUSU9ORzYnLSUpQk9VTkRTX1hHNiMkIiIhISIiLSUpQk9VTkRTX1lHNiMkIiIhISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlK1MhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlK1MhIiItJSlDSElMRFJFTkc2Ig==Ig==

Hyquadser(3)

KytJInlHNiIsJComIiIlIiIiKSIiJCNGKCIiI0YoRigiIiEsJComIyIkWyIiI0ZGKEYpRihGKEYoLCQqJiMiJTNaIiRIKEYoRilGKEYoRiwtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKEYq

evalf(coeff(%,y,j)/GAMMA(-4/3))

JCIrJT4hUnJPISIq

J1Yovertsing:=series(subs(Z=Zsing, J1Yovertsol),epsilon,6)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS1KMVlvdmVydHNpbmdHRigsNiomIyIjSyIiKiIiIikiIiQjRjMiIiNGM0YzKiojIiIpRjVGMylJKGVwc2lsb25HRigjRjdGNUYzKUY3I0YzRjVGM0Y0RjMhIiIqKEY5RjNGNEYzRjxGM0YzKipGPUYzKUY8IyIiJUY1RjNGNEYzKUY3Rj1GM0YzKiojIiNFRjJGMylGPCMiIiZGNUYzRj5GM0Y0RjNGQCooIyIjJCkiI09GM0Y0RjMpRjxGN0YzRjMqKiMiIzwiIz1GMylGPCMiIihGNUYzRjRGM0ZGRjNGMyoqIyIldEQiJGspRjMpRjxGOUYzRj5GM0Y0RjNGQCooIyIkLCQiJFciRjNGNEYzKUY8RjVGM0YzLUkiT0dGJTYjKiQpRjwjIiM1RjVGM0YzNyNGLg==

Bovertsing:=simplify(series(subs(Z=Zsing, Bovertsol),epsilon,6))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStCb3ZlcnRzaW5nR0YoLDAtSSJPR0YlNiMqJClJKGVwc2lsb25HRigjIiM1IiIkIiIiRjgqKiMiIiVGN0Y4KUY0IyIiI0Y3RjgpRj4jRjhGN0Y4KUY3I0Y4Rj5GOEY4KipGPUY4KUY0RjpGOEZBRjgpRj5GPUY4RjgqKiMiIzgiIipGOClGNCMiIiZGN0Y4Rj9GOEZBRjhGOCoqIyIjPCIjPUY4KUY0IyIiKEY3RjhGQUY4RkVGOEY4KiojIiV0RCIlRzxGOClGNCMiIilGN0Y4Rj9GOEZBRjhGOCooI0Y4RldGOCwqKiYiJSd5KkY4KUY0RjdGOEY4KiYiJiNSNUY4KUY0Rj5GOEY4KiYiJj86IkY4RjRGOEY4IiZnYCJGOEY4RkFGOEY4NyNGLg==

Expression of (D(y)+2/t^2/(1+y)^2) exprrootTV

LCQqNiMiIzsiIiQiIiIpSSJURzYiI0YmIiIjRidJIlZHRipGJywmRi1GJ0YnISIiRicsJkYtRidGJ0YnRicsSiomKUYpRiZGJylGLSIiJUYnRicqKEY1RidGM0YnKUYtRiZGJ0YvKiYpRilGLEYnRjRGJ0YnKigiIidGJ0YzRicpRi1GLEYnRicqKCIjN0YnRjlGJ0Y3RidGLyooIiImRidGKUYnRjRGJ0YvKihGNUYnRjNGJ0YtRidGLyooIiNRRidGOUYnRjxGJ0YnKihGNUYnRilGJ0Y3RidGJyomRiZGJ0Y0RidGJyokRjNGJ0YnKihGPkYnRjlGJ0YtRidGLyooRixGJ0YpRidGPEYnRicqJkY+RidGN0YnRicqJEY5RidGJyooRjVGJ0YpRidGLUYnRicqJiIjPUYnRjxGJ0YnKiZGQEYnRilGJ0YvKiZGPkYnRi1GJ0YnRiZGJ0YnKSwqKiZGKUYnRi1GJ0YnRilGL0YtRi9GJkYvRixGJyksJkYpRidGJkYnRiZGLywyKiZGOUYnRjxGJ0YnKihGLEYnRjlGJ0YtRidGL0ZIRidGSkYnKiZGJkYnRjxGJ0YvKiZGLEYnRilGJ0YnKiZGO0YnRi1GJ0YvRiZGL0YvKSwuKiZGKUYnRjxGJ0YnKihGLEYnRilGJ0YtRidGLyokRjxGJ0YvRilGJyomRixGJ0YtRidGL0YnRi9GLEYvRi8=

n:=16: factor(series(subs(V=Vser(n),T=Tser(n),exprrootTV),t,n+1))

Ky9JInRHNiIsJComIyIiIyIiJCIiIiksJkYqRipJInlHRiRGKkYoISIiRiohIiNGJyIiISwmIyIjNUYpRioqJiMiIiVGKUYqRi1GKkYqRigsKCMiIycpRilGKiomIyIjY0YpRipGLUYqRioqJkY2RiopRi1GKEYqRipGNiwqIyIkJSkpRilGKiomIyIkQyhGKUYqRi1GKkYqKiYiIyEqRipGPkYqRioqJiMiI1NGKUYqKUYtRilGKkYqIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRioiIik=

exprsingP:=map(factor,series(subs(V=Vsing,T=Tsing, exprrootTV),epsilon,2))

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

b1:=factor(subs(epsilon=1,op(2,exprsingP)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNiMUdGKCwkKjAjIiM7IiNGIiIiKSIiJCNGMyIiI0YzLCZJIlBHRihGM0YzRjNGMylGNyNGM0Y1RjMpLCZGOUYzRjUhIiJGN0YzKUY5RjVGMyksJkY5RjNGM0Y+IiImRj5GMzcjRi4=

evalf(GAMMA(-2/3))

JCErMHlTPVMhIio=

algb1:=factor(resultant(numer(bb1-b1),algP,P)); collect(%,bb1,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdiMUdGKCw6KigiJ2MpSCciIiIpSSRiYjFHRigiIiRGMSlJInlHRigiIidGMUYxKioiKGMxKj5GMSkiIiMjRjtGNEYxRjNGMSlGNkY0RjFGMSooIighR1xKRjFGMkYxKUY2IiImRjEhIiIqKCIoYzlIJ0YxKUY0I0YxRjtGMUY2RjFGQioqIihvPihmRjFGOkYxRjNGMSlGNkY7RjFGQiooIihnJilIJ0YxRjJGMSlGNiIiJUYxRjEqJkZERjFGRUYxRkIqKkZIRjFGOkYxRjNGMUY2RjFGMSooRktGMUYyRjFGPUYxRkIqKEY5RjFGOkYxRjNGMUZCKihGP0YxRjJGMUZJRjFGMSooRjBGMUYyRjFGNkYxRkI3I0Yu

LCgqKiInYylIJyIiIkkieUc2IkYlKSwmRiZGJUYlISIiIiImRiUpSSRiYjFHRiciIiRGJUYlKioiKGMxKj5GJSkiIiMjRjJGLkYlKUYpRi5GJUYtRiVGJSooIihjOUgnRiUpRi4jRiVGMkYlLCZGJUYlRiZGJUYlRio=

HyP:=-2^(5/3)*b1

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRIeVBHRigsJCouIyIjayIjRiIiIikiIiQjRjMiIiNGMywmSSJQR0YoRjNGM0YzRjMpLCZGOUYzRjUhIiJGN0YzKUY5RjVGMyksJkY5RjNGM0Y8IiImRjxGPDcjRi4=

yP

LCQqKCwmKiYiIiQiIiJJIlBHNiJGJ0YnRichIiJGJylGKCIiI0YqLCZGKEYnRiZGKkYqRio=

Let us check N:=80:j:=0: plot([seq([1/n,coeff(coeff(Dser(N),y,j),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.1,ord=2..3,style=point);

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NiI=

series(subs(P=Pser(3),HyP),y,2)

KylJInlHNiIsJComIyIkNyYiIyIpIiIiKSIiJCNGKiIiI0YqRioiIiEsJComIyImR0QjIiUoPSNGKkYrRipGKkYqLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRipGLg==

evalf(-op(1,%)/GAMMA(-2/3))

JCIrIXpIWHMjISIq

N:=80:j:=1: plot([seq([1/n,coeff(coeff(Dser(N),y,j),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.1,ord=2..4.5,style=point);

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Ig==

series(subs(P=Pser(3),HyP),y,2)

KylJInlHNiIsJComIyIkNyYiIyIpIiIiKSIiJCNGKiIiI0YqRioiIiEsJComIyImR0QjIiUoPSNGKkYrRipGKkYqLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRipGLg==

evalf(-coeff(%,y,1)/GAMMA(-2/3))

JCIrc1coKlJXISIq

N:=80:j:=2: plot([seq([1/n,coeff(coeff(Dser(N),y,j),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.1,ord=2..6.5,style=point);

NistJSdDVVJWRVNHNiQ3XHA3JCQiIzUhIiIkIiIhISIiNyQkIiImISIiJCIiISEiIjckJCIrTExMTEwhIzUkIiIhISIiNyQkIiNEISIjJCIrNzghXGQiISM1NyQkIiIjISIiJCIiISEiIjckJCIrbm1tbTshIzUkIitXbjdgViEjNTckJCIrSDlkRzkhIzUkIiIhISIiNyQkIiREIiEiJCQiK3dvSEh2ISM1NyQkIis2NjY2NiEjNSQiIiEhIiI3JCQiIiIhIiIkIipBOiFwNSEiKTckJCIrIjQ0NDQqISM2JCIiISEiIjckJCIrTExMTCQpISM2JCIqRFZrTyIhIik3JCQiKyNwMkJwKCEjNiQiIiEhIiI3JCQiK1ZyJkc5KCEjNiQiK0gwXVI7ISIqNyQkIitubW1tbSEjNiQiIiEhIiI3JCQiJEQnISIlJCIrKlsxdik9ISIqNyQkIjIxKys1JUhOIyllISM9JCIiISEiIjckJCIrY2JiYmIhIzYkIit1eic9NiMhIio3JCQiKyYqeTpqXyEjNiQiIiEhIiI3JCQiIiYhIiMkIitwNnU5QiEiKjckJCIraVohPnclISM2JCIiISEiIjckJCIrWFhYWFghIzYkIitGRVYpXCMhIio3JCQiKygzRXlNJSEjNiQiIiEhIiI3JCQiK25tbW1UISM2JCIrN0A5bEUhIio3JCQiIiUhIiMkIiIhISIiNyQkIitZUTpZUSEjNiQiK0dVJ28iRyEiKjckJCIrL1BxLlAhIzYkIiIhISIiNyQkIityJkc5ZCQhIzYkIitYSk9iSCEiKjckJCIraWVGW00hIzYkIiIhISIiNyQkIitMTExMTCEjNiQiKzApekAzJCEiKjckJCIrX2shZUEkISM2JCIiISEiIjckJCIlREohIiYkIio+XycpPiQhIik3JCQiKi4uLi4kISM1JCIiISEiIjckJCIrcms8VEghIzYkIitCJlJmSSQhIio3JCQiK2RHOWRHISM2JCIiISEiIjckJCIreXh4eEYhIzYkIisjPlldUyQhIio3JCQiKy5GcS1GISM2JCIiISEiIjckJCIrWip5OmojISM2JCIrRE8lb1wkISIqNyQkIitrRDVrRCEjNiQiIiEhIiI3JCQiI0QhIiQkIitsJiozI2UkISIqNyQkIipSQyFSQyEjNSQiIiEhIiI3JCQiKyJRXzRRIyEjNiQiK3pZV2hPISIqNyQkIismUiJlREIhIzYkIiIhISIiNyQkIit0c3NzQSEjNiQiKypvJ1tOUCEiKjckJCIrQUFBQUEhIzYkIiIhISIiNyQkIitWSSJSPCMhIzYkIisjUUFaIVEhIio3JCQiK3UmZnc3IyEjNiQiIiEhIiI3JCQiK0xMTCQzIyEjNiQiKzB4ZnBRISIqNyQkIitGaiIzLyMhIzYkIiIhISIiNyQkIiIjISIjJCIrQ2pdSVIhIio3JCQiKzlWeWc+ISM2JCIiISEiIjckJCIrQnAyQj4hIzYkIitSb3ooKVIhIio3JCQiK2BDeicpPSEjNiQiIiEhIiI3JCQiK189Jj0mPSEjNiQiK3ApeTwvJSEiKjckJCIrPT09PT0hIzYkIiIhISIiNyQkIisnRzlkeSIhIzYkIitVI0dGNCUhIio3JCQiK2xmUWE8ISM2JCIiISEiIjckJCIrSno4QzwhIzYkIislUSIqMzklISIqNyQkIithXyJccCIhIzYkIiIhISIiNyQkIitubW1tOyEjNiQiK2QhKlsnPSUhIio3JCQiK2lVTVI7ISM2JCIiISEiIjckJCIrRUshSGgiISM2JCIrcyY+KEhVISIqNyQkIisoZSx0ZSIhIzYkIiIhISIiNyQkIiZEYyIhIickIitCOndxVSEiKjckJCIrUTpZUTohIzYkIiIhISIiNyQkIis6Ojo6OiEjNiQiK1loeDRWISIqNyQkIis4dGAjXCIhIzYkIiIhISIiNyQkIitOIyllcTkhIzYkIithJDRwTSUhIio3JCQiK2lgRlw5ISM2JCIiISEiIjckJCIrSDlkRzkhIzYkIisoXCRII1ElISIqNyQkIisvMlgzOSEjNiQiIiEhIiI3JCQiKyopKSkpKSlRIiEjNiQiKyMpKVtnVCUhIio3JCQiKzlJJylwOCEjNiQiIiEhIiI3JCQiK144Tl44ISM2JCIrLV5HW1chIio3JCQiK0xMTEw4ISM2JCIiISEiIjckJCIrdSUqeTo4ISM2JCIrJD4tInpXISIqNyQkIisqSCwoKUgiISM2JCIiISEiIjckJCIrI0deP0ciISM2JCIrVTtmM1ghIio3JCQiKyZ5QWVFIiEjNiQiIiEhIiI3JCQiJEQiISIlJCIrWFxdLlkhIiotJSZDT0xPUkc2JyUkUkdCRyQiKUMpZXElISIpJCIiISEiIiQiKCc+IVwmISIpLSUrX0FUVFJJQlVURUc2Iy8lJ3NvdXJjZUclLG1hdGhkZWZhdWx0Ry0lJVZJRVdHNiQ7JCIiISEiIiQiIiIhIiI7JCIjPyEiIiQiI2whIiItJiUmX0FYSVNHNiMiIiI2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0mJSZfQVhJU0c2IyIiIzYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUrQVhFU0xBQkVMU0c2JC1JI21pRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNjVRJGFiczYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EmZmFsc2U2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdub3JtYWw2Ii1JI21pRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNjVRJG9yZDYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EldHJ1ZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ2l0YWxpYzYiLSUmU1RZTEVHNiMlJlBPSU5URy0lKV9WSVNJQkxFRzYjIiIiLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIkIWYhIiItJSlCT1VORFNfWUc2IyQiI10hIiItJS1CT1VORFNfV0lEVEhHNiMkIiUhPiQhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlK04hIiItJSlDSElMRFJFTkc2Ii0lK0FOTk9UQVRJT05HNictJSlCT1VORFNfWEc2IyQiIiEhIiItJSlCT1VORFNfWUc2IyQiIiEhIiItJS1CT1VORFNfV0lEVEhHNiMkIiUrUyEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUrUyEiIi0lKUNISUxEUkVORzYiRzYi

series(subs(P=Pser(3),HyP),y,3)

KytJInlHNiIsJComIyIkNyYiIyIpIiIiKSIiJCNGKiIiI0YqRioiIiEsJComIyImR0QjIiUoPSNGKkYrRipGKkYqLCQqJiMiJ3d4RSImJG8+RipGK0YqRipGLi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YqRiw=

evalf(-coeff(%,y,2)/GAMMA(-2/3))

JCIrIW8wUidlISIq

exprrootTU

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

n:=16: factor(series(subs(U=User(n),T=Tser(n),exprrootTU),t,n+1))

KytJInRHNiIsJCooIyIiIiIiJEYoLCZJInhHRiRGKEYoISIiRihGK0YsRiwhIiMsJComRidGKEYrRihGKCIiISwkKihGJ0YoRitGKCwmRilGKEYrRihGKEYoIiIjLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiU=

exprsingM:=map(factor,series(subs(U=Using,T=Tsing, exprrootTU),epsilon,1))

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

b1:=(subs(epsilon=1,op(2,exprsingM)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNiMUdGKCwkKi4iI0siIiIsJiokKUkiTUdGKCIiI0YxRjEiIiQhIiJGMSlGNyNGMUY2RjEpRjYjRjFGN0YxLChGM0YxKiYiIzdGMUY1RjFGOCIiKkYxRjgpLCZGNUYxRjdGOEY2RjhGMTcjRi4=

evalf(GAMMA(-2/3))

JCErMHlTPVMhIio=

algb1:=factor(resultant(numer(bb1-b1),algM,M)); collect(%,bb1,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdiMUdGKCwwKigiKltzWnonIiIiKSIiJCNGMSIiI0YxKUkieEdGKCIiJUYxISIiKioiKlszKlxARjEpRjUjRjVGM0YxSSRiYjFHRihGMUY2RjFGMSoqIisleUUqPjxGMUY8RjFGPkYxKUY3RjNGMUY5KioiK29OJilSTUYxRjxGMUY+RjEpRjdGNUYxRjEqKCIrbzZSKTMiRjEpRj5GM0YxRkRGMUY5KigiK1ckSHJxKUYxRkdGMUY3RjFGMSomIiwpb2VVVDxGMUZHRjFGOTcjRi4=

LCgqKCIrbzZSKTMiIiIiKSwmSSJ4RzYiRiUiIiUhIiIiIiNGJSlJJGJiMUdGKSIiJEYlRisqLCIqWzMqXEBGJSlGLCNGLEYvRiVGJkYlKUYoRixGJUYuRiVGJSooIipbc1p6J0YlKUYvI0YlRixGJSlGKEYqRiVGKw==

HxL:=-2^(5/3)*subs(M=L,b1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRIeExHRigsJCosIiRHIiIiIiwmKiQpSSJMR0YoIiIjRjFGMSIiJCEiIkYxKUY3I0YxRjZGMSwoRjNGMSomIiM3RjFGNUYxRjgiIipGMUY4KSwmRjVGMUY3RjhGNkY4Rjg3I0Yu

algL:=subs(x=4*x,M=L,algM)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGdMR0YoLCwqKCIiKSIiIkkieEdGKEYxKUkiTEdGKCIiJEYxRjEqJiwmKiYiJDMiRjFGMkYxISIiIiNPRjFGMSlGNCIiI0YxRjEqKCIkOyNGMUYyRjFGNEYxRjFGOEY6RjlGOjcjRi4=

xL:=factor(solve(algL,x))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN4TEdGKCwkKioiIioiIiIsJiokKUkiTEdGKCIiI0YxRjEiIiQhIiJGMSwmKiZGNkYxRjVGMUYxRjdGOEY4LChGM0YxKiYiIzdGMUY1RjFGOEYwRjFGOEY4NyNGLg==

factor(HxL/xL)

LCQqKiMiJEciIiIqIiIiKSIiJCNGJyIiI0YnKSwmSSJMRzYiRidGKSEiIkYrRjAsJiomRitGJ0YuRidGJ0YpRjBGJ0Yn

Hxser:=proc(n) map(expand,map(rationalize,series(subs(L=Lser(n),HxL),x,4))) end

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZIeHNlckdGKGYqNiNJIm5HRihGKEYoRigtSSRtYXBHRiY2JEknZXhwYW5kR0YmLUYyNiRJLHJhdGlvbmFsaXplR0YlLUknc2VyaWVzR0YmNiUtSSVzdWJzR0YmNiQvSSJMR0YoLUklTHNlckdGKEYvSSRIeExHRihJInhHRigiIiVGKEYoRig3I0Yu

Let us check N:=120:i:=1: ser:= Cser(N): plot([seq([1/n,coeff(coeff(coeff(convert(ser,polynom),x,-i),y,0),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.05,ord=1.5..1.8,style=point);

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Ig==

Hxser(2)

KydJInhHNiIjIiNrIiIqIiIiLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiM=

evalf(-coeff(%,x,i)/GAMMA(-2/3))

JCIrNFNqcDwhIio=

i:=2: plot([seq([1/n,coeff(coeff(coeff(convert(ser,polynom),x,-i),y,0),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.05,ord=0.5..2,style=point);

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

Hxser(3)

KylJInhHNiIjIiNrIiIqIiIiLCQqJiMiJGMjIiMiKUYoKSIiJCNGKCIiI0YoRihGMS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRi8=

evalf(-coeff(%,x,2)/GAMMA(-2/3))

JCIrJipbRWk4ISIq

i:=3: plot([seq([1/n,coeff(coeff(coeff(convert(ser,polynom),x,-i),y,0),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.05,ord=0.5..1.5,style=point);

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

Hxser(4)

KytJInhHNiIjIiNrIiIqIiIiLCQqJiMiJGMjIiMiKUYoKSIiJCNGKCIiI0YoRihGMSwmKiYjIiQ3JkYtRihGLkYoRihGNCEiIkYvLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiU=

evalf(-coeff(%,x,3)/GAMMA(-2/3))

JCIrJHlAOjoiISIq

HxL;HyP

LCQqLCIkRyIiIiIsJiokKUkiTEc2IiIiI0YlRiUiIiQhIiJGJSlGLCNGJUYrRiUsKEYnRiUqJiIjN0YlRilGJUYtIiIqRiVGLSksJkYpRiVGLEYtRitGLUYt

LCQqLiMiI2siI0YiIiIpIiIkI0YnIiIjRicsJkkiUEc2IkYnRidGJ0YnKSwmRi1GJ0YpISIiRitGJylGLUYpRicpLCZGLUYnRidGMSIiJkYxRjE=

Hfinal:=(HxL+HyP*(1+y-2*x*y))/(1+y+x^2*y+x^2*y^2-4*x*y)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdIZmluYWxHRigqJiwmKiwiJEciIiIiLCYqJClJIkxHRigiIiNGMkYyIiIkISIiRjIpRjgjRjJGN0YyLChGNEYyKiYiIzdGMkY2RjJGOSIiKkYyRjkpLCZGNkYyRjhGOUY3RjlGOSowIyIjayIjRkYyRjpGMiwmSSJQR0YoRjJGMkYyRjIpLCZGR0YyRjhGOUY3RjIpRkdGOEYyKSwmRkdGMkYyRjkiIiZGOSwoKihGN0YySSJ4R0YoRjJJInlHRihGMkY5RlFGMkYyRjJGMkY5RjIsLComKUZQRjdGMilGUUY3RjJGMiomRlRGMkZRRjJGMiooIiIlRjJGUEYyRlFGMkY5RlFGMkYyRjJGOTcjRi4=

n:=5:ser:=map(Z->factor(expand(rationalize(Z))),mtaylor(subs(P=Pser(n),L=Lser(n),Hfinal),[x,y],4))

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

evalf(%)

LDYkIit4ciNbNCIhIikiIiIqJiQiKzY2NjZyISIqRiZJInhHNiJGJkYmKiYkIiszRzsleSJGJUYmSSJ5R0YsRiZGJiomJCIrKCllOHVhRipGJilGKyIiI0YmRiYqKCQiK1dLYXk5RiVGJkYrRiZGMEYmRiYqJiQiK05rTmNCRiVGJilGMEY1RiZGJiomJCIrPlRHRllGKkYmKUYrIiIkRiZGJiooJCIreU8/LTdGJUYmRjRGJkYwRiZGJiooJCIrckJ5KjMjRiVGJkYrRiZGPEYmRiYqJiQiK0RoIVsnR0YlRiYpRjBGQUYmRiY=

Non-boundary coefficients serdiff:=mtaylor(subs(P=Pser(n),L=Lser(n),ser-HyP-HxL),[x,y],4)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShzZXJkaWZmR0YoLCgqKiMiI2siIyIpIiIiLCYiIiohIiIqJiIjO0YzKSIiJCNGMyIiI0YzRjNGM0kieEdGKEYzSSJ5R0YoRjNGMyoqIyIkYyMiI0ZGMywmKiRGOUYzRjNGOkY2RjMpRj1GPEYzRj5GM0Y2KiojRjEiJSg9I0YzLCYiJFYjRjMqJiIkcyNGM0Y5RjNGM0YzRj1GMylGPkY8RjNGMzcjRi4=

let us check these coefficients N:=120:k:=1:l:=1: plot([seq([1/n,coeff(coeff(coeff(convert(Cser(N),polynom),x,l-k),y,l),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.05,ord=2.5..4,style=point);

NistJSdDVVJWRVNHNiQ3ZHI3JCQiIzUhIiIkIiNEISIjNyQkIiImISIiJCIiISEiIjckJCIrTExMTEwhIzUkIitHT052KCkhIzU3JCQiI0QhIiMkIiIhISIiNyQkIiIjISIiJCIrYSV5P00iISIqNyQkIitubW1tOyEjNSQiIiEhIiI3JCQiK0g5ZEc5ISM1JCIrR1NieDshIio3JCQiJEQiISIkJCIiISEiIjckJCIrNjY2NjYhIzUkIitzLUhHPiEiKjckJCIiIiEiIiQiIiEhIiI3JCQiKyI0NDQ0KiEjNiQiK3N3PkFAISIqNyQkIitMTExMJCkhIzYkIiIhISIiNyQkIisjcDJCcCghIzYkIisiei1sRiMhIio3JCQiK1ZyJkc5KCEjNiQiIiEhIiI3JCQiK25tbW1tISM2JCIrOks/LUMhIio3JCQiJEQnISIlJCIiISEiIjckJCIyMSsrNSVITiMpZSEjPSQiK2FyZjFEISIqNyQkIitjYmJiYiEjNiQiIiEhIiI3JCQiKyYqeTpqXyEjNiQiK2lEcSVmIyEiKjckJCIiJiEiIyQiIiEhIiI3JCQiK2laIT53JSEjNiQiK1J6MnFFISIqNyQkIitYWFhYWCEjNiQiIiEhIiI3JCQiKygzRXlNJSEjNiQiK1teSk5GISIqNyQkIitubW1tVCEjNiQiIiEhIiI3JCQiIiUhIiMkIitcaE0jeiMhIio3JCQiK1lROllRISM2JCIiISEiIjckJCIrL1BxLlAhIzYkIisjSFNFJUchIio3JCQiK3ImRzlkJCEjNiQiIiEhIiI3JCQiK2llRltNISM2JCIrVlxMKClHISIqNyQkIitMTExMTCEjNiQiIiEhIiI3JCQiK19rIWVBJCEjNiQiKkhDdCNIISIpNyQkIiVESiEiJiQiIiEhIiI3JCQiKi4uLi4kISM1JCIrKTRATCdIISIqNyQkIityazxUSCEjNiQiIiEhIiI3JCQiK2RHOWRHISM2JCIrXzAhZipIISIqNyQkIit5eHh4RiEjNiQiIiEhIiI3JCQiKy5GcS1GISM2JCIrej5gREkhIio3JCQiK1oqeTpqIyEjNiQiIiEhIiI3JCQiK2tENWtEISM2JCIrdkBnX0khIio3JCQiI0QhIiQkIiIhISIiNyQkIipSQyFSQyEjNSQiKz5HVnhJISIqNyQkIisiUV80USMhIzYkIiIhISIiNyQkIismUiJlREIhIzYkIitVT0grSiEiKjckJCIrdHNzc0EhIzYkIiIhISIiNyQkIitBQUFBQSEjNiQiKmE3OTckISIpNyQkIitWSSJSPCMhIzYkIiIhISIiNyQkIit1JmZ3NyMhIzYkIisnUiQpNDkkISIqNyQkIitMTEwkMyMhIzYkIiIhISIiNyQkIitGaiIzLyMhIzYkIis3QTxmSiEiKjckJCIiIyEiIyQiIiEhIiI3JCQiKzlWeWc+ISM2JCIraT43d0ohIio3JCQiK0JwMkI+ISM2JCIiISEiIjckJCIrYEN6Jyk9ISM2JCIrbWsmPj4kISIqNyQkIitfPSY9Jj0hIzYkIiIhISIiNyQkIis9PT09PSEjNiQiKyZbJHkxSyEiKjckJCIrJ0c5ZHkiISM2JCIiISEiIjckJCIrbGZRYTwhIzYkIipGKHA/SyEiKTckJCIrSno4QzwhIzYkIiIhISIiNyQkIithXyJccCIhIzYkIiszMXlMSyEiKjckJCIrbm1tbTshIzYkIiIhISIiNyQkIitpVU1SOyEjNiQiK0RsNVlLISIqNyQkIitFSyFIaCIhIzYkIiIhISIiNyQkIisoZSx0ZSIhIzYkIisjb1J4RCQhIio3JCQiJkRjIiEiJyQiIiEhIiI3JCQiK1E6WVE6ISM2JCIrXHZ0b0shIio3JCQiKzo6Ojo6ISM2JCIiISEiIjckJCIrOHRgI1wiISM2JCIrcjg6ekshIio3JCQiK04jKWVxOSEjNiQiIiEhIiI3JCQiK2lgRlw5ISM2JCIrMHEtKkckISIqNyQkIitIOWRHOSEjNiQiIiEhIiI3JCQiKy8yWDM5ISM2JCIrJ2YwJSlIJCEiKjckJCIrKikpKSkpKVEiISM2JCIiISEiIjckJCIrOUknKXA4ISM2JCIrJj1DdEkkISIqNyQkIiteOE5eOCEjNiQiIiEhIiI3JCQiK0xMTEw4ISM2JCIrKT47ZUokISIqNyQkIit1JSp5OjghIzYkIiIhISIiNyQkIisqSCwoKUgiISM2JCIreT0iUkskISIqNyQkIisjR14/RyIhIzYkIiIhISIiNyQkIismeUFlRSIhIzYkIipuUTtMJCEiKTckJCIkRCIhIiUkIiIhISIiNyQkIissemNNNyEjNiQiKz46LVJMISIqNyQkIismPjcmPjchIzYkIiIhISIiNyQkIit4Iz5bPyIhIzYkIitmSjNZTCEiKjckJCIqPncvPiIhIzUkIiIhISIiNyQkIispZXFrPCIhIzYkIipPV0dOJCEiKTckJCIrKXAhemk2ISM2JCIiISEiIjckJCIrKEdEJVw2ISM2JCIrQFRLZkwhIio3JCQiK09PT082ISM2JCIiISEiIjckJCIrMWJmQjYhIzYkIittKVJiTyQhIio3JCQiKzY2NjY2ISM2JCIiISEiIjckJCIrKjQsKik0IiEjNiQiKzJ3XXJMISIqNyQkIitBbCZwMyIhIzYkIiIhISIiNyQkIis8KW9fMiIhIzYkIit0P0N4TCEiKjckJCIrKHlIUTEiISM2JCIiISEiIjckJCIrejpqXzUhIzYkIitWb3YjUSQhIio3JCQiK25tbVQ1ISM2JCIiISEiIjckJCIrTnkjNC4iISM2JCIqWWshKVEkISIpNyQkIitqIjMvLSIhIzYkIiIhISIiNyQkIiosLCwsIiEjNSQiK0NsPCRSJCEiKjckJCIiIiEiIyQiIiEhIiI3JCQiKyo0ISo0ISoqISM3JCIrelA1KVIkISIqNyQkIitwOiNSISkqISM3JCIiISEiIjckJCIra3l0MygqISM3JCIrKj1jR1MkISIqNyQkIis6WVE6JyohIzckIiIhISIiNyQkIitDJjRRXyohIzckIis6SVcyTSEiKjckJCIra0EnUlYqISM3JCIiISEiIjckJCIrJFIlelgkKiEjNyQiKihHKD1UJCEiKTckJCIrZiNmI2YjKiEjNyQiIiEhIiI3JCQiK0Y+SnUiKiEjNyQiK3dQOjtNISIqNyQkIisiNDQ0NCohIzckIiIhISIiNyQkIis0ITQhNCEqISM3JCIrN0tIP00hIio3JCQiK0g5ZEcqKSEjNyQiIiEhIiI3JCQiK0F2YlwpKSEjNyQiK24iKUhDTSEiKjckJCIrRClIPngpISM3JCIiISEiIjckJCIrdUBsJnApISM3JCIqPHYiR00hIik3JCQiK2InKm8/JykhIzckIiIhISIiNyQkIitaJjNxYSkhIzckIitLLiQ+ViQhIio3JCQiK3JpZHUlKSEjNyQiIiEhIiI3JCQiMSoqKioqXE1oTFMpISM9JCIrJFFwYlYkISIqNyQkIjEsKytMTExMJCkhIz0kIiIhISIiLSUmQ09MT1JHNiclJFJHQkckIilDKWVxJSEiKSQiIiEhIiIkIignPiFcJiEiKS0lK19BVFRSSUJVVEVHNiMvJSdzb3VyY2VHJSxtYXRoZGVmYXVsdEctJSVWSUVXRzYkOyQiIiEhIiIkIiImISIjOyQiI0QhIiIkIiNTISIiLSYlJl9BWElTRzYjIiIiNiYtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJiUmX0FYSVNHNiMiIiM2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lK0FYRVNMQUJFTFNHNiQtSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1USRhYnM2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJmZhbHNlNiIvJSp1bmRlcmxpbmVHUSZmYWxzZTYiLyUqc3Vic2NyaXB0R1EmZmFsc2U2Ii8lLHN1cGVyc2NyaXB0R1EmZmFsc2U2Ii8lK2ZvcmVncm91bmRHUShbMCwwLDBdNiIvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XTYiLyUnb3BhcXVlR1EmZmFsc2U2Ii8lK2V4ZWN1dGFibGVHUSZmYWxzZTYiLyUpcmVhZG9ubHlHUSZmYWxzZTYiLyUpY29tcG9zZWRHUSZmYWxzZTYiLyUqY29udmVydGVkR1EmZmFsc2U2Ii8lK2ltc2VsZWN0ZWRHUSZmYWxzZTYiLyUscGxhY2Vob2xkZXJHUSZmYWxzZTYiLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lLG1hdGh2YXJpYW50R1Enbm9ybWFsNiItSSNtaUc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY1USRvcmQ2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2Ii0lJlNUWUxFRzYjJSZQT0lOVEctJSlfVklTSUJMRUc2IyIiIi0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJFMoISIiLSUpQk9VTkRTX1lHNiMkIiRTIiEiIi0lLUJPVU5EU19XSURUSEc2IyQiJVNJISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJT9NISIiLSUpQ0hJTERSRU5HNiItJStBTk5PVEFUSU9ORzYnLSUpQk9VTkRTX1hHNiMkIiIhISIiLSUpQk9VTkRTX1lHNiMkIiIhISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlK1MhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlK1MhIiItJSlDSElMRFJFTkc2Ig==Ig==

evalf(-coeff(coeff(serdiff,x,k),y,l)/GAMMA(-2/3))

JCIrd2JVek8hIio=

N:=120:k:=2:l:=1: plot([seq([1/n,coeff(coeff(coeff(convert(Cser(N),polynom),x,l-k),y,l),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.05,ord=2.5..3,style=point);

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NiI=

serdiff

LCgqKiMiI2siIyIpIiIiLCYiIiohIiIqJiIjO0YnKSIiJCNGJyIiI0YnRidGJ0kieEc2IkYnSSJ5R0YyRidGJyoqIyIkYyMiI0ZGJywmKiRGLUYnRidGLkYqRicpRjFGMEYnRjNGJ0YqKiojRiUiJSg9I0YnLCYiJFYjRicqJiIkcyNGJ0YtRidGJ0YnRjFGJylGM0YwRidGJw==

evalf(-coeff(coeff(serdiff,x,k),y,l)/GAMMA(-2/3))

JCIrXDh1IipIISIq

N:=120:k:=1:l:=2: plot([seq([1/n,coeff(coeff(coeff(convert(Cser(N),polynom),x,l-k),y,l),t,n)/4^(n)*n^(5/3)],n=1..N)],abs=0..0.05,ord=2.5..6,style=point);

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

serdiff

LCgqKiMiI2siIyIpIiIiLCYiIiohIiIqJiIjO0YnKSIiJCNGJyIiI0YnRidGJ0kieEc2IkYnSSJ5R0YyRidGJyoqIyIkYyMiI0ZGJywmKiRGLUYnRidGLkYqRicpRjFGMEYnRjNGJ0YqKiojRiUiJSg9I0YnLCYiJFYjRicqJiIkcyNGJ0YtRidGJ0YnRjFGJylGM0YwRidGJw==

evalf(-coeff(coeff(serdiff,x,k),y,l)/GAMMA(-2/3))

JCIrdExfK18hIio=

JSFH