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ABSTRACT
This is a research work on the theory and application of the Gamma and Beta function for solving scientific and engineering problems. Frantic effort was devoted to ensure clarity of the underlying ideas so that users will not ignorantly misconstrue the use of Gamma and Beta functions. To start with the origin of factorial, the mother of Gamma function was investigated. It was discovered that Gamma function came into existence as a result of the quest to generalize the factorial function for non-integers values.
The nexus of gamma and beta function was considered because of its importance in problems solving. The Bohr-Mollarup theorem which shows the uniqueness of gamma function was considered, as a well as the various relations sanctified by gamma function. We went further to apply gamma functions to resolve some definite integral. It was shown also that gamma and beta functions have relevance in Bessel and hyper geometric functions.
Lastly we were able to show the application of gamma and beta function in Engineering such as James Stirling’s approximation, wave propagation, integration problem, calculating products, analytic number theory, and gamma and beta distributions and their various applications were considered.
