simplify_sum



 More simpler example

(%i1) load(simplify_sum)$
(%i2) S:sum_by_integral(1/((2*n-1)^2+1),n,1,inf)$

(%i3) simplify_sum(S);
(%o3) (%i*(psi[0]((-%i-1)/2+1)+%gamma))/4-(%i*(psi[0]((%i-1)/2+1)+%gamma))/4

(%i4) expand(%);
(%o4) (%i*psi[0](1/2-%i/2))/4-(%i*psi[0](%i/2+1/2))/4

 How convert this to   1/4*%pi*tanh(1/2*%pi)     ?

Aleksas D