Séries trigonométricas e funções de Bessel : aspectos históricos do século XVIII

Abstract

The present work was developed within the framework of a bibliographical review consisting of books and scientific articles that discuss the history of the so-called Bessel functions, and aimed to follow the path of its development until its consolidation as a class of special functions in the fourteenth century. Its multiplicity of applications, ranging from wave equations to problems of celestial mechanics, made these functions appear in the works of several famous names in science, even before Friedrich Wilhelm Bessel found them in his studies on planetary motion. . In addition, this monograph studied Bessel's biography, focusing mainly on his contributions to Mathematics, and some of the problems to which he dedicated himself. Kepler's problem is highlighted here, for which a simplified approach to the one developed by Bessel will be presented, making use of his method of expansion in trigonometric series.