Generalização da integral de Fresnel

Abstract

In the literature, there are several classes and techniques for computing improper integrals, such as residue theory, change of order of integration, Laplace transforms, etc. In this article, we will present an analytical expression for the generalization of one of the Fresnel integrals, for this, we will use Laplace transforms, change of order of integration and identities involving beta and gamma functions. We believe that the development of alternative techniques to Analytically calculating improper integrals is of paramount importance for the understanding of theory and for the improvement of current techniques.