Theorem 12.3 (Fourier Cosine Series). Assume that is an even function and has period . If are piecewise continuous, the Fourier series for     involves only the cosine terms,  ,  and we write  

        ,  

where .  

Proof.

Proof of Theorem 12.3 is left for the reader in the book.

Complex Analysis for Mathematics and Engineering

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