Integrais impróprias em intervalos ilimitados com parâmetros complexos

Abstract

The understanding of the convergence of improper integrals is important for the study of integral transforms, especially the Laplace transform. In this sense, the following work studies some aspects of improper integration in unlimited intervals with complex parameters. A review of concepts such as limit, derivative and integral in the domain of complex numbers is carried out, using tools of mathematical analysis and differential and integral calculus. Then, some fundamental theorems about the convergence of improper integrals are demonstrated, such as the comparison criterion, the Cauchy criterion and the convergence of the integral that defines the Laplace transform. Other results quite uncommon to be found in the literature are presented. Finally, some special integral transforms are presented.