On a Generalization of Kummer’s Second-Type F 1 1 and F 2 2

Abstract

The aim of this paper is to establish a general form of Kummer’s second-type summation theory. By defining a new form for the divided of the Pochhammer symbol d + i n / d n , we can develop a general form of Kummer’s second-type summation theorem as e − x / 2 F 2 2 a , i + d ; x b + l , d ; in the form of a sum of e − x / 2 F 1 1 a ; x b + i ; for i , l = 0,1,2 , … , Then, some properties of the generalized Kummer’s second-type summation theorem can yield a number of known and novel results.