NOTE ON CONVERGENCE OF EULER'S GAMMA FUNCTION

Abstract

The Gamma function <TEX>${\Gamma}$</TEX> which was first introduced b Euler in 1730 has played a very important role in many branches of mathematics, especially, in the theory of special functions, and has been introduced in most of calculus textbooks. In this note, our major aim is to explain the convergence of the Euler's Gamma function expressed as an improper integral by using some elementary properties and a fundamental axiom holding on the set of real numbers <TEX>$\mathbb{R}$</TEX>, in a detailed and instructive manner. A brief history and origin of the Gamma function is also considered.