Generalizations of Gauss's second summation theorem and Bailey's formula for the series $_2 F_1 (1/2)$
Commun. Korean Math. Soc. 2006 Vol. 21, No. 3, 569-575 Printed September 1, 2006
Arjun K. Rathie, Yong Sup Kim, Junesang Choi Govt. Sujangarh College, WonKwang University, Dongguk University
Abstract : We aim mainly at presenting two generalizations of the well-known Gauss's second summation theorem and Bailey's formula for the series $_2F_1 (1/2)$. An interesting transformation formula for $_p F_q$ is obtained by combining our two main results. Relevant connections of some special cases of our main results with those given here or elsewhere are also pointed out.
Keywords : generalized hypergeometric series $_p F_q$, summation theorems for $_p F_q$