Relations and Identities for Gamma and Gauss Hypergeometric Functions Appilication of the Gamma Function.

Abstract

Equations involving the gamma and hypergeometric functions are of great interest to math ematicians and scientists, and newly proven identities for these functions assist in finding solutions to differential and integral equations. The term hypergeometric function was intro duced by John Wall in his book 1655,which also appear in the work of Euler,Gauss,Riemann and Kummer.However, the firist in-depth treatement was executed by Gauss in1813.In this work we trace a brief history of the development of the gamma and hypergeometric func tions, illustrate the close relationship between them and present range of their most useful properties and identities, from the earliest ones to thosedeveloped in more recen years. Our literature review will show that while continuedresearch into hypergeometric identities has generated many new results, some ofthese can be shown to be variations of known identities.