# multiplication formula for gamma function

For any integer $n>0$, the gamma function^{} satisfes the following relation:

$$\mathrm{\Gamma}(nz)={(2\pi )}^{\frac{n-1}{2}}{n}^{nz-\frac{1}{2}}\prod _{k=0}^{n-1}\mathrm{\Gamma}\left(z+\frac{k}{n}\right)$$ |

This equation is true for all complex values of $z$ for which both sides are defined.

Title | multiplication formula for gamma function |
---|---|

Canonical name | MultiplicationFormulaForGammaFunction |

Date of creation | 2013-03-22 14:44:08 |

Last modified on | 2013-03-22 14:44:08 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 8 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 33B15 |

Classification | msc 30D30 |