• Title/Summary/Keyword: ${\tau}$-Lauricella functions of several variables

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SOME τ-EXTENSIONS OF LAURICELLA FUNCTIONS OF SEVERAL VARIABLES

  • KALLA, SHYAM LAL;PARMAR, RAKESH KUMAR;PUROHIT, SUNIL DUTT
    • Communications of the Korean Mathematical Society
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    • v.30 no.3
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    • pp.239-252
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    • 2015
  • 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.