I'm reading an article and he just state:
let $f\left(\theta,\varphi\right)$ be of this form $$f\left(\theta,\varphi\right)={\sum}g_{m}\left(\theta\right)e^{im\varphi},$$
I'm on the unitary sphere, may I say that all continuous functions may be written in this form or there's some assumptions underlying it? I guessed could be just something like the Fourier Series of a function in spherical coordinates but I didn't know the result.