The Gamma Function and Its Analytical Applications

This paper explores the history and properties of the Gamma function with some analytical applications. Specifically, the Gamma function is employed to prove the legitimacy of the Standard Normal Distribution and for evaluation of some integrals involving the Laplace and Fourier Transforms using very simple techniques. Moreover, this paper demonstrates that the Gamma function is not a mere formula and proof in itself but rather an essential tool for applications in evaluating integrals that occur in practice and also in simplifying proofs of some other important identities and theorems in mathematics.