A note on Gauss's second summation theorem for the series $_2 F_1 (1/2)$

Commun. Korean Math. Soc. 2007 Vol. 22, No. 4, 509-512 Printed December 1, 2007

Junesang Choi, Arjun K. Rathie, Purnima Dongguk University, Govt. P. G. College, Govt. Dungar College (Bikaner University)

Abstract : We aim at deriving Gauss's second summation theorem for the series $_2 F_1 (1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

Keywords : generalized hypergeometric series $_p F_q$, Gauss's second summation theorem for $_2 F_1 (1/2)$, Beta function