Summation of Certain Infinite Series by the Approach of Partial Fractions and Hypergeometric Functions

Abstract

In the present article, we have obtained the summations of certain infinite series by using partial fraction approach, some hypergeometric summation theorems of positive and negative unit arguments, Digamma, trigamma, tetragamma, Riemann Zeta functions, lower case beta function of one-variable and other associated functions. We have also obtained some new hypergeometric summation theorems of positive and negative unit arguments.