On some generalizations of Ramanujan's continued fraction identities
type: Item
instance of: scholarly article
title: On some generalizations of Ramanujan's continued fraction identities
zbMATH Open document ID: 0656.10005
DOI: 10.1007/BF02837811
author: S. H. Smith
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: Many of the continued fraction expansions of Ramanujan can be viewed as special cases of the expansion of the ratio of basic hypergeometric series: \(_ 2\phi_ 1(a,b;c;xq)/_ 2\phi_ 1(a,b;c;x).\) The authors find the related expansions for the ratios in which the numerator has been replaced by one of a number of similar basic hypergeometric series.
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4070992
zbMATH Keywords: identities
zbMATH Keywords: q-continued fractions
zbMATH Keywords: Rogers-Ramanujan continued fractions
zbMATH Keywords: continued fraction expansions
zbMATH Keywords: ratio of basic hypergeometric series
reviewed by: David M. Bressoud
MaRDI profile type: Publication
cites work: Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series
cites work: An Introduction to Ramanujan's "lost" Notebook
cites work: Ramanujan's ``lost'' notebook. III: The Rogers-Ramanujan continued fraction
cites work: Chapter 12 of Ramanujan's second notebook: Continued fractions
cites work: On Some Continued Fraction Identities of Srinivasa Ramanujan
cites work: Q3682543
cites work: A short note on generic initial ideals
cites work: A New Class of Continued Fraction Expansions for the Ratios of Heine Functions
cites work: A continued fraction
cites work: Q3864588
cites work: Ramanujan's continued fraction
cites work: Q5513003
full work available at URL: https://doi.org/10.1007/bf02837811
OpenAlex ID: W2019394773
description: scientific article; zbMATH DE number 4070992