MODELING AND IMPLEMENTATION OF A PROGRAM FOR COMPUTING THE FACTORIAL OF FRACTIONAL NUMBERS USING THE GAMMA FUNCTION

Abstract

This article provides information about the origin and application of the Gamma function. Formulas for calculating the factorial of fractional numbers using the Gamma function have been derived. A program was developed in the Python programming language to compute the results. The outcomes of manual calculations and the program's results have been compared.

The Gamma function is considered one of the major mathematical objects. The origin of the Gamma function dates back to the 18th century. The Gamma function is associated with the name of Leonhard Euler, as he was the first to introduce the fundamental ideas of the Gamma function in his scientific research. Euler realized the need to generalize the factorial for real numbers and aimed to define the Gamma function. Through this function, he achieved significant results in studying problems such as multi-dimensional integrals, infinite series, and analytic continuation. Later, based on Euler’s work, Legendre made a substantial contribution to shaping the key properties of the Gamma function. For this reason, in some sources, the Gamma function is also referred to as the Euler-Legendre function.