For Laplace’s equation inside a circular disk (r ≤ a), using (2.5.45) and (2.5.47), show...

For Laplace’s equation inside a circular disk (r ≤ a), using (2.5.45) and (2.5.47), show that

Using cos z = Re [e^iz], sum the resulting geometric series to obtain Poisson’s integral formula.

Reference 2.5.45:

Reference 2.5.47: