Abstract
Srivastava noticed the existence of three additional complete triple hypergeometric functions <TEX>$H_A$</TEX>, <TEX>$H_B$</TEX> and <TEX>$H_C$</TEX> 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 <TEX>$H_A$</TEX> and <TEX>$H_C$</TEX>. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava's <TEX>$H_C$</TEX> with the help of generalized Dixon's theorem and generalized Whipple's theorem on the sum of a <TEX>$_3F_2$</TEX> obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
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