Fourier series

Diriclet Conditions

Theorem:

Suppose that

(1) $f(x)$ is defined and single-valued except possibly at a finite number of points in $(-L,L)$

(2) $f(x)$ is periodic outside $(-L,L)$ with period $P=2L$

(3) $f(x)$ and $f^{\prime }(x)$ are piecewise continuous in $(-L,L)$.