SOME τ-EXTENSIONS OF LAURICELLA FUNCTIONS OF SEVERAL VARIABLES

Title & Authors
SOME τ-EXTENSIONS OF LAURICELLA FUNCTIONS OF SEVERAL VARIABLES
KALLA, SHYAM LAL; PARMAR, RAKESH KUMAR; PUROHIT, SUNIL DUTT;

Abstract
Motivated mainly by certain interesting extensions of the $\small{{\tau}}$-hypergeometric function defined by Virchenko et al. [11] and some $\small{{\tau}}$-Appell's function introduced by Al-Shammery and Kalla [1], we introduce here the $\small{{\tau}}$-Lauricella functions $\small{F_A^{(n),{\tau}_1,{\cdots},{\tau}_n}}$, $\small{F_B^{(n),{\tau}_1,{\cdots},{\tau}_n}}$ and $\small{F_D^{(n),{\tau}_1,{\cdots},{\tau}_n}}$ and the confluent forms $\small{{\Phi}_2^{(n),{\tau}_1,{\cdots},{\tau}_n}}$ and $\small{{\Phi}_D^{(n),{\tau}_1,{\cdots},{\tau}_n}}$ of n variables. We then systematically investigate their various integral representations of each of these $\small{{\tau}}$-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 $\small{{\tau}}$-hypergeometric function;Appell's and Lauricella functions;$\small{{\tau}}$-Appell's function;$\small{{\tau}}$-Lauricella functions of several variables;generating function;
Language
English
Cited by
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