Theorem 12.7 (The Dirichlet problem in  D). If has period and has the Fourier series representation

            ,  

then the solution to the Dirichlet problem in  the unit disk D is  

(12.11)            ,  

where denotes a complex number in the closed disk .  

Proof.

Proof of Theorem 12.7.

Proof of Theorem 12.7 is in the book.

Complex Analysis for Mathematics and Engineering

(c) 2006 John H. Mathews, Russell W. Howell