On Product Formulas of Guillera and Sondow
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 eγ. We describe formulas for the products in terms of special values of the Hurwitz zeta function ζ(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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