Some hypergeometric and other evaluations of \(\zeta (2)\) and allied series
type: Item
instance of: scholarly article
title: Some hypergeometric and other evaluations of \(\zeta (2)\) and allied series
zbMATH Open document ID: 0965.11039
DOI: 10.1016/S0096-3003(98)10082-6
author: Junesang Choi
author: Arjun K. Rathie
author: H. M. Srivastava
published in: Applied Mathematics and Computation
publication date: 2001-08-05T00:00:00Z
review text: Numerous interesting solutions of the problem of evaluating \(\zeta(2)\) \((:= \sum_{k=1}^\infty k^{-2})\), which was of vital importance to Euler and the Bernoulli brothers (James and John Bernoulli), have appeared in the mathematical literature ever since Euler first solved this problem in 1736. The main object of this note is to present yet another evaluation of \(\zeta(2)\) and related sums by applying the theory of hypergeometric series. Some other approaches to this problem are also indicated.
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 1355408
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: Basler problem
zbMATH Keywords: Gauss' summation theorem
zbMATH Keywords: Wallis' integral formula
zbMATH Keywords: Dixon's summation theorem
zbMATH Keywords: evaluation of \(\zeta(2)\)
zbMATH Keywords: hypergeometric series
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
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full work available at URL: s0096-3003(98)10082-6
OpenAlex ID: W2026056118
description: scientific article; zbMATH DE number 1355408