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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}]

enter image description here enter image description here

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?

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  • $\begingroup$ 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}]. $\endgroup$ – J. M. will be back soon Jan 31 '17 at 16:33
  • $\begingroup$ 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. $\endgroup$ – Feyre Jan 31 '17 at 16:35
  • $\begingroup$ ...or if there's one, it's a solution Mathematica doesn't know. $\endgroup$ – J. M. will be back soon Jan 31 '17 at 16:36

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