Dirichlet's conditions

The three conditions on a periodic function that guarantee its Fourier series converges.

Dirichlet's conditions on one period of $f$ are three requirements: finitely many discontinuities, finitely many local maxima and minima, and both one-sided limits existing at every point. A function meeting all three is called piecewise smooth; nearly every function this course builds a Fourier series from qualifies.

Examples

A square wave satisfies Dirichlet's conditions: one jump and no wild oscillation per period.