# Error computing sum “Infinite expression 1/0 encountered”

I am trying to calculate a symbolic sum.The expression is defined as follows:

 Sum[(Zeta[-m]*Pochhammer[m - n - 1, n]*x^m)/m!, {m, 1, Infinity},
Assumptions -> {x > 0, n >= 0, n \[Element] Integers}]


If I put:

(Zeta[-m]*Pochhammer[m - n - 1, n]*x^m)/m! /. m -> 1
(* -(1/12) x Pochhammer[-n, n] *)


is Ok.

Any idea what could be happening here?

• If I use an alternate expression in terms of Binomial[], I no longer get an error, but the sum returns unevaluated: Sum[(Zeta[-m] n! Binomial[m - 2, n] x^m)/m!, {m, 1, Infinity}]. – J. M. will be back soon Jan 31 '17 at 16:33
• For the Sum[], the algorithm changes it into the version with the Gamma[] function, which fails at m=1. Unfortunately, staring at m=2 returns the Sum[] unevaluated. Add this to @J.M. 's comment, and I suspect no solution exists. Even though the series does seem to converge. – Feyre Jan 31 '17 at 16:35
• ...or if there's one, it's a solution Mathematica doesn't know. – J. M. will be back soon Jan 31 '17 at 16:36