On the definition of the Euler Gamma function

  • Ricardo Pérez-Marco

    Université de Paris, France
On the definition of the Euler Gamma function cover

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Abstract

We present a new definition of the 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.

Cite this article

Ricardo Pérez-Marco, On the definition of the Euler Gamma function. Enseign. Math. 68 (2022), no. 1/2, pp. 135–160

DOI 10.4171/LEM/1023