SU\G(𝔸)/K·U

On Product Formulas of Guillera and Sondow

Shihan Kanungo, Jordan Schettler

Type: Preprint

Publication Date: 2024-10-09

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2410.07534

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.

Locations

  • arXiv (Cornell University) - View - PDF

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