A Certain Series Associated with Catalan’s Constant

Abstract

A parametric class of series generated by integration of complete elliptic integrals ${\sum }_{–r\ne k=0}^{\infty }\frac{\left(\begin{array}{c}2k\\ k\end{array}\right)}{(k+r)16^k}$ is valuated in closed form. Alternative proofs to results of Ramanujan and others are given. Also, a particular case of the Saalschützian hypergeometric series ${}_4{F}_3(1)$ is derived.