The potential field outside of a charged hemispherical shell

I have a hemispherical shell of radius a held at potential Vo. Using Laplace’s equation, with appropriate boundary conditions, I’ve been able to find the potential at any point within the hemisphere as:

U(r,$Theta$) = $sum_{n=0}^infty B_n (frac ra)^n P_n[cosTheta]$

where r is radial distance from the centre of the hemisphere
$Theta$ is polar angle
$B_n$ is a coefficient determinable from initial conditions
$P_n$ is the legendre polynomial wrt cos$Theta$

How would one go about calculating the potential outside of this hemisphere at any point? Could the general result above be useful?

Thanks in advance.