On several new contiguous function relations for $k$-hypergeometric function with two parameters

Sivamani Chinra; Vilfred Kamalappan; Medhat A. Rakha; Arjun K. Rathie

doi:10.4134/CKMS.c160167

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2017; 32(3): 637-651

Online first article April 12, 2017 Printed July 31, 2017

https://doi.org/10.4134/CKMS.c160167

On several new contiguous function relations for $k$-hypergeometric function with two parameters

Sivamani Chinra, Vilfred Kamalappan, Medhat A. Rakha, and Arjun K. Rathie

Central University of Kerala, Central University of Kerala, Suez Canal University, Central University of Kerala

Abstract

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Abstract

Very recently, Mubeen, et al.~\cite{5} have obtained fifteen contiguous function relations for $k$-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for $k$-hypergeometric functions with two parameters. Obviously, for $k\rightarrow 1$ we recover the results obtained by Cho, et al.~\cite{2} and Rakha, et al.~\cite{7}.

Keywords: contiguous function relations, $k$-hypergeometric functions

MSC numbers: 33C05, 33D15