Communications of the
Korean Mathematical Society CKMS

In 1997, Exton, by mainly employing a widely-used process of resolving hypergeometric series into odd and even parts, obtained some new and interesting summation formulas with arguments $1$ and $-1$. We aim at showing how easily many summation formulas can be obtained by simply combining some known summation formulas. Indeed, we present 22 results in the form of two generalized summation formulas for the generalized hypergeometric series $_4 F_3$, including two Exton's summation formulas for $_4 F_3$ as special cases.

Keywords: generalized hypergeometric series $_p F_q$, summation theorems for $_p F_q$

MSC numbers: Primary 33C20, 33C60; Secondary 33C70, 33C65