Using V1 I was able to put Bn in terms of An, so the sum now looks like
V(r,𝜃) = sum n=0 to infinity A_n (r^n - b^(2n+1)/(r^(n+1))) P_n(cos𝜃)
I'm not sure how to proceed after writing out the new sum equal to V2, V3. How do I use the Legendre polynomials? for 𝜃 = pi/2 i know Pn(cos𝜃) leaves...
I'm having troubles setting up this problem. I know we are to use boundary conditions to determine An and Bn since in this case (a<r<b) neither can be set to 0. I don't know how the given potentials translate into boundary conditions, especially the V3 disk.