# Dirichlet conditions

Let $f$ be a piecewise http://planetmath.org/node/1146regular real-valued function defined on some interval $[a,b]$, such that $f$ has only a finite number of discontinuities and extrema in $[a,b]$. Then the Fourier series^{} of this function converges to $f$ when $f$ is continuous^{} and to the arithmetic mean^{} of the left-handed and right-handed http://planetmath.org/node/2950limit of $f$ at a point where it is discontinuous^{}.

Title | Dirichlet conditions |
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Canonical name | DirichletConditions |

Date of creation | 2013-03-22 13:21:53 |

Last modified on | 2013-03-22 13:21:53 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 6 |

Author | mathwizard (128) |

Entry type | Theorem |

Classification | msc 42A20 |

Related topic | FourierSeriesOfFunctionOfBoundedVariation |

Related topic | FourierCoefficients |