Communications of the
Korean Mathematical Society
CKMS

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

Article

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Commun. Korean Math. Soc. 2018; 33(4): 1159-1170

Printed October 31, 2018

https://doi.org/10.4134/CKMS.c170327

Copyright © The Korean Mathematical Society.

Some properties of extended $\tau$-hypergeometric function

Ranjan Kumar Jana, Bhumika Maheshwari, Ajay Kumar Shukla

S. V. National Institute of Technology, S. V. National Institute of Technology, S. V. National Institute of Technology

Abstract

Recently, Parmar \cite{Parmar2015} introduced a new extension of the $\tau$-Gauss hypergeometric function ${}_2R_1^\tau (z)$. The main object of this paper is to study this extended $\tau$-Gauss hypergeometric function and obtain its properties including connection with modified Bessel function of third kind and extended generalized hypergeometric function, several contiguous relations, differential relations, integral transforms and elementary integrals. Various special cases of our results are also discussed.

Keywords: hypergeometric function, Gamma and Beta functions, contiguous relations, integral transforms

MSC numbers: 33B15, 33C05, 33C20