Theorem 12.4 (Fourier Sine Series). Assume that is an odd function and has period . If are piecewise continuous, the Fourier series for     involves only the sine terms,  ,  and we write  

        ,  

where  .  

Proof.

Proof of Theorem 12.4 is left for the reader in the book.

Complex Analysis for Mathematics and Engineering

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