JournalszaaVol. 21, No. 3pp. 817–826

A Certain Series Associated with Catalan’s Constant

  • V.S. Adamchik

    Carnegie Mellon University, Pittsburgh, USA
A Certain Series Associated with Catalan’s Constant cover
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Abstract

A parametric class of series generated by integration of complete elliptic integrals rk=0(2kk)(k+r)16k\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 4F3(1)_4F_3(1) is derived.

Cite this article

V.S. Adamchik, A Certain Series Associated with Catalan’s Constant. Z. Anal. Anwend. 21 (2002), no. 3, pp. 817–826

DOI 10.4171/ZAA/1110