A derivative we have to evaluate in Lemma 17

>    unassign('m'):

>    Jexpr:=proc(m)
subs(yinv=1/y,C=CC,CC^(m/2) *TT(xsubs) ):end:

>    Jexpr(m);

((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2*m)*TT(-1/2*(nu-1)*(-4+q)/((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2)/y+1/2*(2*nu-2+q)/((q*nu-2*nu+1+...
((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2*m)*TT(-1/2*(nu-1)*(-4+q)/((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2)/y+1/2*(2*nu-2+q)/((q*nu-2*nu+1+...
((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2*m)*TT(-1/2*(nu-1)*(-4+q)/((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2)/y+1/2*(2*nu-2+q)/((q*nu-2*nu+1+...
((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2*m)*TT(-1/2*(nu-1)*(-4+q)/((q*nu-2*nu+1+nu^2)*II^2-q*(nu+1)*II+(nu-1)*(-4+q)*(w*q+nu-1)*t+q)^(1/2)/y+1/2*(2*nu-2+q)/((q*nu-2*nu+1+...

Expression of L1(0;y)

>    map(factor,map(simplify,map(normal,subs(t=0,II=0,diff(Jexpr(m),II))),symbolic));

-1/2*q^(1/2*m)*m*(nu+1)*TT(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)+1/4*q^(1/2*m-1/2)*D(TT)(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)*(nu-1)*(-4+q)*(y*nu-nu-1)/y
-1/2*q^(1/2*m)*m*(nu+1)*TT(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)+1/4*q^(1/2*m-1/2)*D(TT)(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)*(nu-1)*(-4+q)*(y*nu-nu-1)/y

>    diff(%,y);

-1/2*q^(1/2*m)*m*(nu+1)*D(TT)(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)*(1/2*(-2*q-4*nu+q*nu+4)/q^(1/2)/y-1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y^2)+1/4*q^(1/2*m-1/2)*`@@`(D,...
-1/2*q^(1/2*m)*m*(nu+1)*D(TT)(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)*(1/2*(-2*q-4*nu+q*nu+4)/q^(1/2)/y-1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y^2)+1/4*q^(1/2*m-1/2)*`@@`(D,...
-1/2*q^(1/2*m)*m*(nu+1)*D(TT)(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)*(1/2*(-2*q-4*nu+q*nu+4)/q^(1/2)/y-1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y^2)+1/4*q^(1/2*m-1/2)*`@@`(D,...
-1/2*q^(1/2*m)*m*(nu+1)*D(TT)(1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y)*(1/2*(-2*q-4*nu+q*nu+4)/q^(1/2)/y-1/2*(4*nu-q*nu-4+q-2*q*y-4*y*nu+y*q*nu+4*y)/q^(1/2)/y^2)+1/4*q^(1/2*m-1/2)*`@@`(D,...

>    map(simplify,collect(factor(limit(%,y=1)),TT,factor),symbolic);

-1/8*q^(1/2*m-1)*(nu-1)^2*(-4+q)^2*`@@`(D,2)(TT)(-1/2*q^(1/2))-1/4*q^(1/2*m-1/2)*(m-1)*(-4+q)*D(TT)(-1/2*q^(1/2))*(-1+nu^2)

>   

>