Fourier's theorem (redirected from Fourier theorem)

Fourier's theorem [‚fu̇r·ē‚āz ‚thir·əm]

(mathematics)

If ƒ(x) satisfies the Dirichlet conditions on the interval -π <x< π, then its Fourier series converges to ƒ(x for all values ofxin this interval at which ƒ(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 ƒ atxand ƒ(x+ 0) is the limit on the right of ƒ atx.