## Solving Laplace's equation in a circular annulus

Problem Statement:

General solution:

Fourier series:

where $r_{1}=a$, $r_{2}=b$, $f_{1}(\theta)=sin(\theta)$, and $f_{2}(\theta)=2sin(\theta)cos(\theta)$.

By evaluating the Fourier series shown above, I determined that $a_{o}=b_{o}=a_{n}=b_{n}=c_{n}=d_{n}=0$.

Is this correct?