About the Laplace series

Abstract

The solution to one of the main problems of mathematical physics, namely the Dirichlet problem for a sphere, is reduced, as is known, to the question of expanding the so-called “arbitrary” function of two angles into a series arranged according to the spherical Laplace functions. The possibility of expansion for a function that has two first derivatives has been proven and reasoning similar to that given in our article: “On the theory of trigonometric series”. It is possible to establish the possibility of expansion for a function that satisfies Lipchitz’s condition.