If ƒ (x ) satisfies the Dirichlet conditions on the interval -π<x< π, then its Fourier series converges to ƒ (x ) for all values of x in this interval at which f (x ) is continuous, and approaches 1/2 [ƒ (x + 0) + ƒ (x - 0)] at points at which ƒ (x ) is discontinuous, where ƒ (x - 0) is the limit on the left of f at x and ƒ (x + 0) is the limit on the right of f at x.