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.
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
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
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