On 7/3/12 7:14 AM, Aleksas Domarkas wrote:
> How simplify sum
>
> sum(4*k^2/(1-2*k+2*k^2)/(1+2*k+2*k^2),k,1,inf); ?
>
> The correct answer is
>
> 1/2*%pi*tanh(1/2*%pi)=integrate(sin(x)/sinh(x),x,0,inf)
>
If you expand the summand, you get something that simplify_sum can
handle. The result involves psi[0] of complex args, and I have no idea
how that can be simplified to your expected result. I can't even use
float and rectform to get a numerical value because the argument of
psi[0] remains (-1)^(1/4).
Yuck.
Ray