Applications of Lehmer’s Infinite Series Involving Reciprocals of the Central Binomial Coefficients

Abstract

The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function Fq+1qz for q=2,3,4,5. This is achieved by means of separating the generalized hypergeometric function Fq+1qz (q=2,3,4,5) into even and odd components together with the use of several known infinite series involving reciprocals of the central binomial coefficients obtained earlier by Lehmer.