2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63435In 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 $Γ_{a,r}(s)$.LaTeX file. 9 pagesNumber Theorytext