On Product Formulas of Guillera and Sondow

Shihan Kanungo; Jordan Schettler

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arXiv · 2410.07534

On Product Formulas of Guillera and Sondow

Shihan Kanungo·Jordan Schettler

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Abstract

In this note, we evaluate a multivariable family of infinite products which generalize Guillera's infinite product for $e$, and Ser's formula (rediscovered by Sondow) for $e^\gamma$. We describe formulas for the products in terms of special values of the Hurwitz zeta function $\zeta(s,u)$ and its $s$ derivative. Additionally, we derive integral and double integral representations for the logarithms of these infinite products.

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Shihan Kanungo, Jordan Schettler. 2024-10-10. On Product Formulas of Guillera and Sondow. https://arxiv.org/abs/2410.07534

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