Hypergeometric series and continued fractions
type: Item
instance of: scholarly article
title: Hypergeometric series and continued fractions
zbMATH Open document ID: 0659.10010
DOI: 10.1007/BF02837830
author: K. G. Ramanathan
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: The use of three term relations among contiguous hypergeometric series to obtain evaluations of continued fractions as a ratio of hypergeometric series is a technique which goes back to Gauss. The author discusses this technique and Ramanujan's use of it, and then employs a q-analog to derive Ramanujan's evaluation of the fraction \[ \frac{1}{1+}\frac{aq+\lambda q}{1+}\frac{bq+\lambda q^ 2}{1+}\frac{aq^ 2+\lambda q^ 3}{1+}\frac{bq^ 2+\lambda q^ 4}{1+}...\quad. \]
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4077319
zbMATH Keywords: hypergeometric series
zbMATH Keywords: continued fractions
zbMATH Keywords: Ramanujan's evaluation
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: On the q-analog of Kummer's theorem and applications
cites work: An Introduction to Ramanujan's "lost" Notebook
cites work: Theq-Gamma andq-Beta Functions†
cites work: Chapter 12 of Ramanujan's second notebook: Continued fractions
cites work: Q3259107
cites work: Q3751658
cites work: Ramanujan's continued fraction
cites work: Q5513003
description: scientific article; zbMATH DE number 4077319