A NEW MODEL FOR GAMMA FUNCTION IN NATURAL NUMBER

به سوی علوم ریاضی

Volume 4, Issue 1 - Serial Number 4, October 2024, Pages 42-64   

Document Type: Expository article (original)

DOI: 10.22067/tmsj.2024.88822.1060

Author

Rostam Mohamadian^*

Department of Mathematics, Faculty of Mathematical and Computer Sciences, Shahid Chamran University of Ahwaz, Ahwaz, IRAN

Abstract

In this article, first, with a simple technique, we obtain a wellknown formula about the gamma function and some theorems of Laplace transforms. After that, we mention a new formula, which can be used to calculate some not so convenient improper integrals, and also with the help of it and the Gaussian integral, we obtain a new convergence result regarding Hermite polynomials. Then with the help of the same formula, we obtain a new model for the gamma function in natural numbers.

Keywords

Power series; Laplace transform; Gamma function; Gauss integral; Hermite polynomials

References