Applications of Lehmer's Infinite Series Involving Reciprocals of the Central Binomial Coefficients. (27th January 2022) - Kumar, B. R. Srivatsa; Kılıçman, Adem; Rathie, Arjun K.
Abstract : The main objective of this paper is to establish several new closed-form evaluations of the generalized hypergeometric function F q + 1 q z for q = 2, 3, 4, 5 . This is achieved by means of separating the generalized hypergeometric function F q + 1 q z (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.