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Letters in Mathematical Physics

, Volume 71, Issue 2, pp 159–171 | Cite as

A Class of Generalized Gamma Functions

  • Jean-Paul Jurzak
Article
  • 61 Downloads

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)

Keywords

Gamma functions infinite products 

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References

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institut de Mathématique de Bourgogne, Faculté des Sciences et TechniquesUniversité de BourgogneDijon CedexFrance

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