On the paper ''a 'lost' notebook of Ramanujan''
type: Item
instance of: scholarly article
title: On the paper ''a 'lost' notebook of Ramanujan''
zbMATH Open document ID: 0539.33003
DOI: 10.1016/0001-8708(84)90027-6
author: R. P. Agarwal
published in: Advances in Mathematics
publication date: 1984-01-01T00:00:00Z
review text: While studying some of the q-series in Ramanujan's lost notebook, Andrews discovered an identity connecting three basic hypergeometric series, two of them special \({}_ 3\phi_ 2's\), the third a special \({}_ 2\phi_ 1\). He raised the question of generalizing this identity and fitting it into the standard work on basic hypergeometric series. Agarwal shows it is a limiting case of a three term relation among \({}_ 3\phi_ 2's\) found by Sears. He also finds a related identity, and applies these identities to obtain further partial theta function identities.
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 3857486
zbMATH Keywords: Ramanujan
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: theta function identities
reviewed by: R. Askey
MaRDI profile type: Publication
full work available at URL: 0001-8708(84)90027-6
OpenAlex ID: W1976376534
cites work: A family of basic hypergeometric and combinatorial identities and certain summation formulae
cites work: An Introduction to Ramanujan's "lost" Notebook
cites work: Ramanujan's ``lost'' notebook. I: Partial Theta-functions
cites work: A Family of Combinatorial Identities
cites work: On the Transformation Theory of Basic Hypergeometric Functions
cites work: Q5508372
cites work: Certain Summation Formulae for Basic Hypergeometric Series
description: scientific article; zbMATH DE number 3857486