General order Euler sums with multiple argument
type: Item
instance of: scholarly article
title: General order Euler sums with multiple argument
zbMATH Open document ID: 1434.11056
published in: Journal of Number Theory
publication date: 2018-05-02T00:00:00Z
full work available at URL: GenOrdMultArgHarNum.pdf
review text: For positive integers \(k,m,p\) let \[ T(k,m,p)=\sum_{n=1}^\infty\frac{H_{pn}^{(m)}}{n}\frac{n+k}{k}. \] In the paper under review the author develops analytic representations for \(T(k,m,p)\) in terms of the the Riemann zeta-function \(\zeta(m)\) and a weighted integral involving hypergeometric function \(_2F_1\). As some examples, the author considers special cases connected with well-known constants. Also, for \(k\geq 2\) he obtains bounds for \(T(k,m,p)\) in terms of polygamma function.
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 6865887
zbMATH Keywords: polygamma function
zbMATH Keywords: integral representation
zbMATH Keywords: logarithmic integral
zbMATH Keywords: Riemann zeta function
author: Anthony Sofo
describes a project that uses: HarmonicSums
MaRDI profile type: Publication
OpenAlex ID: W2792215583
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DOI: 10.1016/J.JNT.2017.12.006
description: scientific article; zbMATH DE number 6865887