Transformation and summation formulas for Kampé de Fériet series \(F^{0:3}_{1:1} (1,1)\)
type: Item
instance of: scholarly article
title: Transformation and summation formulas for Kampé de Fériet series \(F^{0:3}_{1:1} (1,1)\)
zbMATH Open document ID: 0861.33013
author: S. N. Pitre
author: J Van der Jeugt
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-09-30T00:00:00Z
review text: By series manipulations and utilization of some classical results it is shown that the series \[ \sum^\infty_{m,n=0} {{(a)_m (b)_m (c)_m (a')_n (b')_n (c')_n} \over {(d)_{m+n} (e)_m (e')_n m!n!}} \] reduces to a gamma fraction multiplied by a \({}_4 F_3[1]\), if \(a'=d-a\), and one of the conditions (i) \(s=e'\), (ii) \(s=1\wedge -a\in\mathbb{N}\), (iii) \(s=1\wedge -c\in\mathbb{N}\wedge -c'\in\mathbb{N}\), where \(s=d+e-a-b-c\), is satisfied. Some particular cases of the reduction formulas are studied.
Mathematics Subject Classification ID: 33C70
Mathematics Subject Classification ID: 81Q99
zbMATH DE Number: 930243
zbMATH Keywords: hypergeometric summation formulas
zbMATH Keywords: \(9-j\) coefficients
reviewed by: Per W. Karlsson
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0306
OpenAlex ID: W1499718996
DOI: 10.1006/JMAA.1996.0306
description: scientific article; zbMATH DE number 930243