Theorem 12.6  (Termwise Differentiation).  Assume that both    have Fourier series representation and that  

        .  

Then    can be obtained by termwise differentiation of  ,  that is  

        .  

Proof.

Proof of Theorem 12.6 is left for the reader in the book.

Complex Analysis for Mathematics and Engineering

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