Some Convergent Summation Theorems For Appell’s Function F1 Having Arguments −1, 1/2

Abstract

In this paper, we obtain some closed forms of hypergeometric summation theorems for Appell’s function of first kind F1 having the arguments −1, 1/2 with suitable convergence conditions, by adjustment of parameters and arguments in generalized form of first, second and third summation theorems of K¨ummer and others.