Chapter 7 of Ramanujan's second notebook
type: Item
instance of: scholarly article
title: Chapter 7 of Ramanujan's second notebook
zbMATH Open document ID: 0537.10023
DOI: 10.1007/BF02863011
author: Bruce C. Berndt
author: Ron Evans
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1983-01-01T00:00:00Z
review text: Chapter 7 in Ramanujan's second notebook is primarily concerned with Bernoulli numbers, sums of powers, the Riemann zeta-function \(\zeta\) (s), and the gamma function. For each result, the authors give either a proof or references to the literature wherein proofs may be found. One of the results in Chapter 7 which is not new is the functional equation of \(\zeta\) (s). Ramanujan employed an extended definition of Bernoulli numbers as well as his theory of divergent series in his unavailing attempt to give a proof.
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11-03
zbMATH DE Number: 3853194
zbMATH Keywords: Ramanujan's second notebook
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: sums of powers
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: gamma function
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02863011
OpenAlex ID: W2029673020
description: scientific article; zbMATH DE number 3853194