A certain series associated with Catalan's constant
type: Item
instance of: scholarly article
title: A certain series associated with Catalan's constant
zbMATH Open document ID: 1009.33006
DOI: 10.4171/ZAA/1110
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2002-11-13T00:00:00Z
review text: The series \(s(r)=\sum^\infty_{k=0} {{2k\choose k}^2\over (k+r) 16^k}\) was studied by Ramanujan in the cases for which \(r=n\) is a positive integer, and when \(r=n+ \frac 12\) is a half integer. The purpose of the article under review is to study this series in the case when \(r=-n\) is a negative integer, in which case the term \(k=-r\) is omitted from the series defining \(S(r)\). Using contour integration, a formula for \(S(r)\) is given in terms of \(S(\frac 12-r)\) and the harmonic numbers.
reviewed by: Shaun Cooper
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 1827613
zbMATH Keywords: Catalan's constant
zbMATH Keywords: summation of series
zbMATH Keywords: hypergeometric functions
author: V. S. Adamchik
MaRDI profile type: Publication
Wikidata QID: Q56082844
cites work: The Partial Sum of the Coefficients of the Hypergeometric Series
cites work: Q3995284
cites work: Two Results of Ramanujan
cites work: Q3879185
cites work: Note on One of Ramanujan's Theorems
cites work: Some Formulas of Ramanujan, Revisited
cites work: Q5513003
full work available at URL: https://doi.org/10.4171/zaa/1110
OpenAlex ID: W2047443903
description: scientific article; zbMATH DE number 1827613