Spherical Harmonics Homework: Calculate Coeficients & Express Function

[pgerlein]

Homework Statement

Hi! I need help with this. I have to calculate the expression of a function using spherical harmonics. The relevant equations are given below. An example of a function can be f(theta,phi) = sin(theta)... Can you help me to calculate de coeficients and to express the function? Thanks.

Homework Equations

View attachment formulas.doc

The Attempt at a Solution

 

[gabbagabbahey]

Hola pgerlein. Welcome to PF

Why don't you show us what you've tried for your example ($f(\theta,\phi)=sin(\theta)$) and we'll know how to help you better.

To make equation writing easier, this forum supports LaTeX. You can find an introduction to using it by clicking here

 

[pgerlein]

I can´t understand the use of this base (spherical harmonics). If I solve the ecuation that gives the coefficients value, how can I express the function in terms of the spherical harmonics?

 

[AEM]

How would you express a function in terms of a Fourier series, for example? Essentially it's the same idea when you write any function in terms of an infinite series of basis functions.