Sums of alternating products of Riemann zeta values and solution of a Monthly problem

Abstract

We solve problem 11585 proposed by B. Burdick, AMM June-July 2011 {\bf 118} (6), p. 558 for the sum of certain products of Riemann zeta function values. We further point out an alternating sum analog, and then present and prove different alternating sum analogs. In addition, we present summation by parts and other results for the Hurwitz and Riemann zeta functions and for the digamma and trigamma functions.

16 pages, no figures

References in corpus (1)

• Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant

Cited by in corpus (2)

• On an integral involving the digamma function
• Series representation of the Riemann zeta function and other results: Complements to a paper of Crandall