Abstract
We study a family of holomorphic functions defined by infinite products of the form \(\Gamma_{a,r}(s) = \prod_{n} \geq 0 (1 + \frac{1}{a + nr})^{s} (1 + \frac{s}{a + nr})^{-1}\) (a, r real, ar > 0) which generalize Euler’s definition since \(\Gamma (s) = \frac{\Gamma_{1.1(s)}}{s}\) . We obtain analogues of classical formulas (e.g. Gauss multiplication and complement formulas) for these functions Γa,r(s)
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Jurzak, JP. A Class of Generalized Gamma Functions. Lett Math Phys 71, 159–171 (2005). https://doi.org/10.1007/s11005-005-0870-4
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DOI: https://doi.org/10.1007/s11005-005-0870-4