[math-fun] log(eta)ish surprise

In the Mittag-Leffler section, W&W derive an identity equivalent to (1/(x^3*Pi)) - (Pi/(x*(Cosh[x*Pi] - Cos[x*Pi]))) == Sum[(((-1)^k*Csch[k*Pi])/(x^2 + 2*k*x + 2*k^2)), {k, -Infinity, -1}] + Sum[(((-1)^k*Csch[k*Pi])/(x^2 + 2*k*x + 2*k^2)), {k, 1, Infinity] where the two sums just mean sum k/=0. Note the similarity of Csch[k Pi] to Simon's recent summands, especially if you use y/(y^2 - 1) = y/(y - 1) - y^2/(y^2 - 1) . So this sum involves e^(-k pi)/(1-e^(-k pi)) and same(2 k), but with a complex degree of freedom! Analyzing the derivation might enable generalization to e^(-k pi/2)/(1-e^(-k pi/2)), etc. --rwg