A Certain Series Associated with Catalan’s Constant
A Certain Series Associated with Catalan’s Constant
A parametric class of series generated by integration of complete elliptic integrals \sum^\infty_{–r \neq k=0} \frac{\bigl(\begin{smallmatrix} 2k\\ k \end{smallmatrix} \bigr)}{(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 _4F_3(1) is derived.