Multiple harmonic series
type: Item
instance of: scholarly article
title: Multiple harmonic series
zbMATH Open document ID: 0763.11037
author: Michael E. Hoffman
published in: Pacific Journal of Mathematics
publication date: 1992-08-03T00:00:00Z
review text: The author studies series of the form \(\sum n_ 1^{-i_ 1} n_ 2^{-i_ 2}\cdots n_ k^{-i_ k}\), where the summation is extended over integers \(n_ 1>n_ 2>\cdots n_ k\geq 1\) and the exponents satisfy \(i_ j\geq 1\) and \(i_ 1>1\). The special case \(k=1\) is the Riemann zeta function; the case \(k=2\) has been studied by many authors, beginning with Euler. It is shown that these series are related to products of values of the Riemann zeta function. Conjectures are made for identities that may hold in the case of positive integer exponents \(i_ j\).
reviewed by: Tom M. Apostol
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 40055
zbMATH Keywords: multiple harmonic series
zbMATH Keywords: products of values of the Riemann zeta function
zbMATH Keywords: identities
MaRDI profile type: Publication
full work available at URL: pjm.1992.152.275
OpenAlex ID: W2000117364
DOI: 10.2140/PJM.1992.152.275
description: scientific article; zbMATH DE number 40055