Shifted quadratic zeta series
type: Item
instance of: scholarly article
title: Shifted quadratic zeta series
zbMATH Open document ID: 1064.40009
DOI: 10.1155/S0161171204402026
author: Anthony Sofo
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/51361
review text: Summary: It is well known that the Riemann zeta function \(\zeta \big(p\big) =\sum_{n=1}^{\infty}1/n^{p}\) can be represented in closed form for \(p\) an even integer. We define a shifted quadratic zeta series as \(\sum_{n=1}^{\infty}1/\big(4n^{2}-\alpha^{2}\big)^{p}\). In this paper, we determine closed-form representations of shifted quadratic zeta series from a recursion point of view using the Riemann zeta function. We also determine closed-form representations of alternating sign shifted quadratic zeta series.
Mathematics Subject Classification ID: 40C99
Mathematics Subject Classification ID: 40D99
zbMATH DE Number: 2171806
zbMATH Keywords: Riemann zeta function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2171806