Spherical Harmonics

Abstract

From the theory of Fourier series on the unit circle we know that when n = 2, every f ∈ L ²(S) has an expansion of the form

$$f({e^{i\theta }})=\sum\limits_{m = - \infty }^\infty {{a_m}{e^{im\theta }},} $$

where the sum converges in L ²(S). In this chapter we will see that an analogous expansion is valid for functions f ∈ L ²(S) when n > 2, with objects known as spherical harmonics playing the roles of the exponentials e ^imθ.