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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 3, 2002, pp. 817–826
DOI: 10.4171/ZAA/1110

Published online: 2002-09-30

A Certain Series Associated with Catalan’s Constant

V.S. Adamchik[1]

(1) Carnegie Mellon University, Pittsburgh, USA

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.

Keywords: Summation of series, elliptic functions, hypergeometric functions, Catalan’s constant

Adamchik V.S.: A Certain Series Associated with Catalan’s Constant. Z. Anal. Anwend. 21 (2002), 817-826. doi: 10.4171/ZAA/1110