# SOME τ-EXTENSIONS OF LAURICELLA FUNCTIONS OF SEVERAL VARIABLES

• KALLA, SHYAM LAL (Department of Mathematics Vyas Institute of Higher Education) ;
• PARMAR, RAKESH KUMAR (Department of Mathematics Government College of Engineering and Technology) ;
• PUROHIT, SUNIL DUTT (Department of Mathematics Rajasthan Technical University)
• Published : 2015.06.30
• 57 9

#### Abstract

Motivated mainly by certain interesting extensions of the ${\tau}$-hypergeometric function defined by Virchenko et al. [11] and some ${\tau}$-Appell's function introduced by Al-Shammery and Kalla [1], we introduce here the ${\tau}$-Lauricella functions $F_A^{(n),{\tau}_1,{\cdots},{\tau}_n}$, $F_B^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and $F_D^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and the confluent forms ${\Phi}_2^{(n),{\tau}_1,{\cdots},{\tau}_n}$ and ${\Phi}_D^{(n),{\tau}_1,{\cdots},{\tau}_n}$ of n variables. We then systematically investigate their various integral representations of each of these ${\tau}$-Lauricella functions including their generating functions. Various (known or new) special cases and consequences of the results presented here are also considered.

#### Keywords

generalized hypergeometric function;generlalized ${\tau}$-hypergeometric function;Appell's and Lauricella functions;${\tau}$-Appell's function;${\tau}$-Lauricella functions of several variables;generating function

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#### Cited by

1. Some generating functions and properties of extended second Appell function vol.37, pp.1, 2017, https://doi.org/10.5269/bspm.v37i1.30725