Um estudo sobre as func ̧oes Gama e Beta e algumas aplicações

Abstract

In this work, we aim to highlight the Gamma function and the Beta function, whose definitions

are developed through integrals, with properties that can be used in different contexts for appli- cations. These functions were determined by Leonhard Euler, who sought to find an expression

that would result in factorial values, considering that its variable takes on values beyond natural numbers. The research problem consists of how to develop applications through the Gamma and Beta functions. The objective is to develop applications in solving non-trivial integrals, determining examples of integrals that can be solved using the Gamma and Beta functions, as well as addressing the application of these functions in Probability, through the Gamma and Beta distributions, performing calculations according to real-world scenarios. The research has a bibliographic nature, based on the bibliographic survey of books, articles, monographs, and dissertations that cover the theme, with a quantitative approach as it involves the description and collection of numerical data and mathematical theories. The research results show that the Gamma and Beta functions are functions to be considered in the resolution of non-trivial integrals, as they can provide efficient solutions, simplifying extensive calculations in certain cases. In addition to their probabilistic models being useful in the analysis of real-world topics, such as the usage time of mobile phones and sugar content in soft drinks. Their properties are fundamental elements in the development of applications.