# Expansion in spherical harmonics sin(theta)

1. Dec 5, 2007

### Gerenuk

1. The problem statement, all variables and given/known data

I want to expand sin(theta) in spherical harmonics.
Well, actually I want
(3cos^2(theta+45°)-1)*exp(i*(psi+45°))
but I think I could find my mistake by the above simple example.

2. Relevant equations

http://en.wikipedia.org/wiki/Spherical_harmonics

3. The attempt at a solution

I seem to get zero for all coefficients by the integrals from wikipedia.
Can I not expand along an arbitrary axis?

2. Dec 5, 2007

### 2Tesla

The coefficients are not all zero. For instance, the first coefficient is proportional to:

$$f_{0}^0 \alpha \int^{2\pi}_{0}d\phi\int^{\pi}_{0}d\theta sin^{2}(\theta)=\pi^2$$