Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\)
type: Item
instance of: scholarly article
title: Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\)
zbMATH Open document ID: 1225.33005
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2011-09-13T00:00:00Z
review text: The authors provide generalizations of two of Euler's classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function \(_{r+2}F_{r+1}(x)\) when there are additional numerator and denominator parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for \(_{r+1}F_{r+1}(x)\).
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33C15
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33C50
zbMATH DE Number: 5947336
zbMATH Keywords: generalized hypergeometric function
zbMATH Keywords: Euler transformation
zbMATH Keywords: Kummer transformation
author: Allen Richard Miller
author: Richard B. Paris
MaRDI profile type: Publication
full work available at URL: s00033-010-0085-0
OpenAlex ID: W1976149960
Wikidata QID: Q56267216
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DOI: 10.1007/S00033-010-0085-0
description: scientific article; zbMATH DE number 5947336