I am not sure how to start and would like some help on how to solve the following problem:
Show that the solution u(r,theta) of Laplace's equation (nabla^2)*u=0 in the semi-circular region r<a, 0<theta<pi, which vanishes on theta=0 and takes the constant value A on theta=pi and on the curved boundary r=a, is
u(r,theta)=(A/pi)[theta + 2*summation ((r/a)^n*((sin n*theta)/n)])