Another method for a new two-term relation for the hypergeometric function \(_{3}F_{2}\) due to Exton
type: Item
instance of: scholarly article
title: Another method for a new two-term relation for the hypergeometric function \(_{3}F_{2}\) due to Exton
zbMATH Open document ID: 1044.33003
author: Yong Sup Kim
author: Hyeong Kee Song
author: Arjun K. Rathie
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-10T00:00:00Z
review text: In this note the authors give a very short proof of the following two-term relation for the hypergeometric function \(_{3}F_{2}\) of unit argument: \[ _{3}F_{2}\Bigg[\begin{matrix} a,\,b,\,c\\ d,\,e\\ \end{matrix} ; 1 \Bigg]=\frac{\Gamma(e)\Gamma(d+e-a-b-c)} {\Gamma(e-c)\Gamma(d+e-a-b)}\,_{3}F_{2}\Bigg[\begin{matrix} d-a,\,d-b,\,c\\ d,\,d+e-a-b\\ \end{matrix} ; 1 \Bigg]\,. \] This formula had been earlier obtained by \textit{H. Exton} [J. Comput. Appl. Math. 106, No.2, 395-397 (1999; Zbl 0930.33002)], by a different method.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 2085553
zbMATH Keywords: generalized hypergeometric series
zbMATH Keywords: two-term relations
MaRDI profile type: Publication
full work available at URL: j.cam.2003.10.018
OpenAlex ID: W2093894769
cites work: A new two-term relation for the \(_3 F_2\) hypergeometric function of unit argument
cites work: Q5508372
DOI: 10.1016/J.CAM.2003.10.018
description: scientific article; zbMATH DE number 2085553