Simple continued fraction expansions of some values of certain hypergeometric functions.
type: Item
instance of: scholarly article
title: Simple continued fraction expansions of some values of certain hypergeometric functions.
zbMATH Open document ID: 1045.11006
published in: Tsukuba Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: This paper studies regularities in the continued fraction expansions of certain hypergeometric series. More precisely, let \(F(a,b,c;z)\) denote the hypergeometric function defined by the power series \[ F(a,b,c;z)=1 +\frac{ab}{c}+\frac{a(a+1)b(b+1)}{c(c+1)} \frac{z ^2}{ 2!} + \frac{a(a+1)(a+2)b(b+1)(b+2)}{c(c+1)(c+2)} \frac{z ^3}{ 3!} +\cdots, \] where \(a,b,c\) are complex constants and \(c \) does not belong to the set of non-positive integers. The continued fraction expansion of certain values of this hypergeometric function (as well as certain values of the confluent hypergeometric functions) are shown in this paper to present some regularities (in the sense of Hurwitz continued fraction expansions) up to some order in the partial quotients.
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1998410
zbMATH Keywords: hypergeometric series
zbMATH Keywords: elementary functions
zbMATH Keywords: confluent hypergeometric functions
zbMATH Keywords: continued fraction
zbMATH Keywords: Hurwitz continued fractions
author: Takao Komatsu
reviewed by: Valérie Berthé
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496164567
OpenAlex ID: W1901754394
DOI: 10.21099/TKBJM/1496164567
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description: scientific article; zbMATH DE number 1998410