I have a solution to Laplace's equation in the form,

$\displaystyle \psi (r,\theta )=\sum_{l=0}^{\infty }\frac{B_{l}}{r^{l+1}}P_{l}(cos(\theta )))$

I have the following boundary condition,

$\displaystyle \psi (z,0)=\frac{-GM}{\sqrt{z^2+a^2})}$

Expand this in orders of the small parameter $\displaystyle \frac{a}{z}$ up to order $\displaystyle (\frac{a}{z})^{6}$

And also find the values of the $\displaystyle B_{i}$ where i is in the range [0:6]

Would I use a taylor expansion? When I do I don't get the right values of the constants.

Help please!