Theorem 12.2.  If    have Fourier series representations, then their sum    has a Fourier series representation, and the Fourier coefficients of  W  are obtained by adding the corresponding coefficients of  U  and  V.

Proof.

Proof of Theorem 12.2 is left for the reader in the book.

Complex Analysis for Mathematics and Engineering

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