Less simple contiguous function relations for hypergeometric functions
type: Item
instance of: scholarly article
title: Less simple contiguous function relations for hypergeometric functions
zbMATH Open document ID: 0933.33019
DOI: 10.1016/S0377-0427(99)00085-0
author: Robert G. Buschman
published in: Journal of Computational and Applied Mathematics
publication date: 2000-04-04T00:00:00Z
review text: \textit{E. Rainville} [Bull. Am. Math. Soc. 51, 714-722 (1945; Zbl 0063.06380)] called a contiguous function relation simple if the coefficients of the relation are constants otherwise less simple. By a contiguous function is meant a function in which exactly one parameter is shifted by \(\pm 1\) from those of the given function and by a linear recurrence relation, a relation which involves some subsets of the set containing the function along with all its contiguous function relations. Considering hypergeometric functions of several variables for a special set of indices, a linear coefficient contiguous function relation is derived. A set of remarks also given to indicate how various changes can be made to extend the results for repeated index, numerator and denominator, for paired indices, for indices of opposite signs and for Kummer's functions.
Mathematics Subject Classification ID: 33C70
zbMATH DE Number: 1326529
zbMATH Keywords: hypergeometric function
zbMATH Keywords: recurrence relation
reviewed by: K. M. Saksena
MaRDI profile type: Publication
cites work: Q5749563
cites work: Q4396498
cites work: Q5824493
cites work: Q4103811
cites work: The contiguous function relations for _{𝑝}𝐹_{𝑞} with application to Batemean’s 𝐽_{𝑛}^{𝑢,𝜈} and Rice’s 𝐻_{𝑛}(𝜁,𝑝,𝜈)
cites work: Q3345085
full work available at URL: s0377-0427(99)00085-0
OpenAlex ID: W1965485909
description: scientific article; zbMATH DE number 1326529