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A class of generalized gamma functions

Jean-Paul Jurzak
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Abstract

In this paper, we study the holomorphic function defined by the infinite product $Γ_{a,r}(s) =\prod_{n \geq 0} (1 + \frac{1}{a+ nr})^s (1 + \frac{s}{a+nr})^{-1}$ which generalize Euler's definition in the sense that $Γ(s) = \frac{Γ_{1,1}(s)}{s}$. We obtain analogues of the Gauss multiplication formula, complement formula for functions $Γ_{a,r}(s)$.

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Jean-Paul Jurzak. 2002-02-26. A class of generalized gamma functions. https://arxiv.org/abs/math/0202270

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