On Certain Generalizations of Kummer’s Second Summation Theorem

Abstract

The objective of this paper is to obtain certain generalizations (in the forms of explicit representation for Clausen’s hypergeometric function 3F2[a, b, c+ p; c, (1+a+b±m)/2; 1/2], believed to be new) of Kummer’s second summation theorem involving Gauss hypergeometric function 2F1[1/2]. Some results of Kim et al., Rathie and Pog´any are also obtained as special cases of our main findings.