Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.4

Infinite Products Involving ζ(3) and Catalan’s Constant


Yasuyuki Kachi
Department of Mathematics
University of Kansas
Lawrence, KS 66045-7523
USA

Pavlos Tzermias
Department of Mathematics
University of Patras
26500 Rion (Patras)
Greece

Abstract:

We present some infinite product formulas for $e^{\frac{7 \zeta (3)}{\pi^2}}$, $e^{\frac{4G}{\pi}}$ and $e^{\frac{2 G}{\pi} \ \pm \frac{1}{2}}$, where G is Catalan's constant. We relate these formulas to similar ones obtained by Guillera and Sondow in the context of their systematic study of Lerch's transcendent. Our proofs are entirely elementary.

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(Concerned with sequences A002117 A006752.)

Received October 1 2012; revised version received November 13 2012. Published in Journal of Integer Sequences, November 20 2012.

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