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