Homogeneous solutions for a class of singular partial differential equations

Abstract

We recall that a spherical harmonic is a hotnegeneous function of x, y, z of certain degree n which satisfies Laplacc equation. Thus, if V(x,y,z.) is such a function of degree K, then xVx+yVy+zV2 = 7vN{\,y,7,), and = ~ important result in the theory of harmonic functions is that any harmonic function can be expressed in a series involving the spherical harmonics.