Dirichlet condition

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The Dirichlet condition , also called Dirichlet's theorem , is named after Peter Gustav Lejeune Dirichlet and specifies when the Fourier series converges point by point to the output function.

statement

Let be a function defined in the interval that fulfills the following properties:

  1. The interval can be broken down into a finite number of sub-intervals in which is continuous and monotonic.
  2. The (finitely many) points of discontinuity are all of the first kind , that is, there are right and left-hand limit values , and .

Then the Fourier series converges in each to

.

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