User:AboutFace 22/Sandbox

Definitions: I have a 2-Sphere and function Fˣ(θ,φ) defined on it. The function Fˣ is well behaved, it is continuous and differentiable everywhere. The functions F are therefore a function in the Hilbert space on 2-Sphere with the basis consisting of Spherical Harmonics with two indices l & m. Y_\ell^m( \theta, \varphi )