A NEW MODEL FOR GAMMA FUNCTION IN NATURAL NUMBER

Document Type : Expository article (original)

Author

• Rostam Mohamadian

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

10.22067/tmsj.2024.88822.1060

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

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