NOTE ON THE CLASSICAL WATSON'S THEOREM FOR THE SERIES3F2

Abstract

Summation theorems for hypergeometric series <TEX>$_2F_1$</TEX> and generalized hypergeometric series <TEX>$_pF_q$</TEX> play important roles in themselves and their diverse applications. Some summation theorems for <TEX>$_2F_1$</TEX> and <TEX>$_pF_q$</TEX> have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series <TEX>$_3F_2$</TEX>(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].