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Infinite Products Involving $\zeta(3)$ and
Catalan's Constant

Yasuyuki Kachi
Department of Mathematics
University of Kansas
Lawrence, KS 66045-7523
USA
mailto:kachi@math.ku.edukachi@math.ku.edu

Pavlos Tzermias
Department of Mathematics
University of Patras
26500 Rion (Patras)
Greece
mailto:tzermias@math.upatras.grtzermias@math.upatras.gr

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.