On Some Sums of Digamma and Polygamma functions - Version (2017) and Review

Abstract

This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard reference works or the literature, but which periodically arise in applications, are collected, reviewed, listed and developed to the point that a knowledgeable reader could devise a formal proof. Several errors in the literature are corrected

This (2017) version contains major enhancements and additions to the previous (2004) version

References in corpus (2)

• A Series Expansion for Integral Powers of Arctangent
• On Powers of a Hypergeometric Function

Cited by in corpus (4)

• The Clausenian hypergeometric function ${}_3{F}_2$ with unit argument and negative integral parameter differences
• Logarithmic Integrals, Polylogarithmic Integrals and Euler sums
• Determination of some generalised Euler sums involving the digamma function
• Logarithmic Integrals of Airy Functions