I have a solution to Laplace's equation in the form,
\psi (r,\theta )=\sum_{l=0}^{\infty }\frac{B_{l}}{r^{l+1}}P_{l}(cos(\theta )))

I have the following boundary condition,

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

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

And also find the values of the 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!