Communications of the
Korean Mathematical Society CKMS

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