Spherical functions are solutions of the equation
that arises from separating variables in Laplace’s equation Δu = 0 in spherical coordinates. Surface harmonics are the restrictions to the unit sphere of harmonic functions (solutions of Laplace’s equation) in three variables. For surface harmonics, m and ν are non-negative integers. The case m = 0 is Legendre’s equation
with ν a non-negative integer. The solutions to equation (9.0.1) that satisfy the associated boundary conditions are Legendre ...