Solve Laplace's Eqn.

(1/р)(∂u/∂Ф) + (1/р)(∂u/∂р) + (∂u/∂р) = 0

in the semidisc {( р , Ф ): 0<= р <1; -pi < Ф <pi}, w/ boundary conds.

U(1, Ф) = cos Ф.

So far I have

U(р , Ф)= A0 + Σ(n=1, ∞) (р^n)(An cos (n Ф) + Bn sin (n Ф))

Therefore:

U(1, Ф)= A0 + Σ(n=1, ∞) (An cos (n Ф) + Bn sin (n Ф)) Ξ cos Ф.

cos Ф = (3cos(Ф) + cos(3 Ф)) / 4.

I think I need to find the fourier coefficients next but am not sure how to. Thanks.