Summation formulas derived from the Srivastava's triple hypergeometric series $H_C$
Commun. Korean Math. Soc. 2010 Vol. 25, No. 2, 185-191
https://doi.org/10.4134/CKMS.2010.25.2.185
Published online June 1, 2010
Yong Sup Kim, Arjun kumar Rathie, and Junesang Choi
Wonkwang University, Vedant College of Engineering and Technology, and Dongguk University
Abstract : Srivastava noticed the existence of three additional complete triple hypergeometric functions $H_{A}$, $H_{B}$ and $H_{C}$ of the second order in the course of an extensive investigation of Lauricella's fourteen hypergeometric functions of three variables. In 2004, Rathie and Kim obtained four summation formulas containing a large number of very interesting reducible cases of Srivastava's triple hypergeometric series $H_{A}$ and $H_{C}$. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava's $H_{C}$ with the help of generalized Dixon's theorem and generalized Whipple's theorem on the sum of a ${}_{3}F_{2}$ obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
Keywords : triple hypergeometric series $H_{A}$ and $H_{C}$, Appell's function, generalized Dixon's theorem, generalized Whipple's theorem
MSC numbers : Primary 33C20, 33C60, 39A10; Secondary 33C70, 33C65
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