Evaluation of series with Hurwitz and Lerch zeta function coefficients by using Hankel contour integrals

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摘要

We introduce a new technique for evaluation of series with zeta coefficients and also for evaluation of certain integrals involving the logGamma function. This technique is based on Hankel integral representations of the Hurwitz zeta, the Lerch Transcendent, the Digamma and logGamma functions.

论文关键词：Hankel contour,Hurwitz zeta function,Lerch Transcendent,Euler constant,Digamma function,LogGamma integral,Barnes function

论文评审过程：Available online 2 October 2006.

论文官网地址：https://doi.org/10.1016/j.amc.2006.08.061