On the definition of Euler Gamma function

Ricardo Pérez-Marco (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We present a new definition of Euler Gamma function. From the complex analysis and transalgebraic viewpoint, it is a natural characterization in the space of finite order meromorphic functions. We show how the classical theory and formulas develop naturally, and we discuss the relation with other definitions. We show in a companion article, that this definition generalizes to higher gamma functions and provides an unifying framework for their definition which is more natural than the usual Bohr-Mollerup or Lerch approaches.

Mots clés: 2010 Mathematics Subject Classification. Primary: 33B15. Secondary: 30D10; 30D15; 30D30; 39A20 Euler Gamma function

Domaines: Variables complexes [math.CV]

Ricardo Pérez-Marco. On the definition of Euler Gamma function. L'Enseignement Mathématique , 2022, 68, 1/2, pp.135-160. ⟨hal-02437549v2⟩