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Motivated mainly by certain interesting extensions of the $\tau$-hypergeometric function defined by Virchenko {\it et al.~}\cite{Vir-Ka-Za} and some $\tau$-Appell's function introduced by Al-Shammery and Kalla \cite{Al-Ka}, we introduce here the $\tau$-Lauricella functions $F_{A}^{ (n),\tau_{1},\ldots,\tau_{n}}$, $F_{B}^{ (n),\tau_{1},\ldots,\tau_{n}}$ and $F_{D}^{ (n),\tau_{1},\ldots,\tau_{n}}$ and the confluent forms $\Phi_{2}^{ (n),\tau_{1},\ldots,\tau_{n}}$ and $\Phi_{D}^{ (n),\tau_{1},\ldots,\tau_{n}}$ 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.
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참고문헌 (13)
참고문헌 신청
A. H. Al-Shammery / 2000 / An extension of some hypergeometric functions of two variables / Rev. Acad. Canaria Cienc 12 (1-2) : 189 ~ 196
E. D. Rainville / 1960 / Special Functions / Macmillan Company
E. M. Wright / 1933 / On the coffecient of power series having exponential singularities / J. London Math. Soc 8 : 71 ~ 79
E. M. Wright / 1935 / The asymptotic expansion of the generalized hypergeometric functions / J. Lon-don Math. Soc 19 : 286 ~ 293
H. M. Srivastava / 1984 / A Treatise on Generating Functions / Halsted Press
E. D. Rainville / 1960 / Special Functions / Macmillan Company
E. M. Wright / 1933 / On the coffecient of power series having exponential singularities / J. London Math. Soc 8 : 71 ~ 79
E. M. Wright / 1935 / The asymptotic expansion of the generalized hypergeometric functions / J. Lon-don Math. Soc 19 : 286 ~ 293
H. M. Srivastava / 1984 / A Treatise on Generating Functions / Halsted Press
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