On a regular Cauchy problem for the Euler—Poisson—Darboux equation

Abstract

A new method is given for solving the wave equation in space of any odd number of dimensions without making use of any device for evaluating divergent integrals. This gives the clue to a simple method of solving the regular Cauchy problem for the so-called Euler-Poisson-Darboux equation in space of any odd number of dimensions, a problem which has previously only been solved by a very difficult extension of Marcel Riesz’s method.