On the definition of Euler Gamma function
Complex Variables
2023-12-08 v2 Classical Analysis and ODEs
Abstract
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.
Cite
@article{arxiv.2001.04445,
title = {On the definition of Euler Gamma function},
author = {Ricardo Pérez-Marco},
journal= {arXiv preprint arXiv:2001.04445},
year = {2023}
}
Comments
30 pages, 2 figures