Determination of the series c_i
> |
> | factor(series(normal(eqinv),y,1)); |
> | c3sol:=factor(solve(coeff(%,y,-6),c[3])); |
> | factor(series(subs(c[3]=c3sol,normal(eqinv)),y,3)); |
> | c2sol:=collect(solve(coeff(%,y,-4),c[2]),t,factor); |
> | factor(subs(K(0)=0,series(subs(c[3]=c3sol,c[2]=c2sol,normal(eqinv)),y,5))); |
> | c1sol:=collect(solve(coeff(%,y,-2),c[1]),t,factor); |
We ignore the following identity
> | subs(K(0)=0,factor(series(subs(c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,normal(eqinv)),y,6))); |
> | subs(K(0)=0,factor(series(subs(c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,normal(eqinv)),y,7))); |
> | c0sol:=collect(solve(coeff(%,y,0),c[0]),[K,t],factor); |
Equation in K(y) with a single catalytic variable
> | catK1:=factor(subs(c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,c[0]=c0sol,eqinv)); |
Back to the series Q(0,y)
> | catQ1:=factor(subs(K(y)=t^2*y*Q(y),D(K)(0)=t^2*Q(0),`@@`(D,2)(K)(0)=2*t^2*D(Q)(0),catK1)); |
> | collect(-catQ1/27*2/(nu-1)^2/t^3,Q,factor); |
> | collect(%+Q(y),Q,factor); |
> |
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