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SUMMATION FORMULAS DERIVED FROM THE SRIVASTAVA'S TRIPLE HYPERGEOMETRIC SERIES HC

Kim, Yong-Sup;Rathie, Arjun Kumar;Choi, June-Sang

  • Published : 2010.04.30

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 $_3F_2$ 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

References

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