# Hankel contour integral

Hankel’s contour integral is a unit (and nilpotent) for gamma function^{} over $\u2102$. That is,

$$ |

Hankel’s integral is holomorphic with simple zeros in ${\mathbb{Z}}_{\le 0}$. Its path of integration starts on the positive real axis *ad infinitum*, rounds the origin counterclockwise and returns to $+\mathrm{\infty}$. As an example of application of Hankel’s integral, we have

$$\frac{i}{2\pi}{\int}_{\mathcal{C}}{(-t)}^{-\frac{1}{2}}{e}^{-t}\mathit{d}t=\frac{1}{\sqrt{\pi}},$$ |

where the path of integration is the one above mentioned.

Title | Hankel contour integral |
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Canonical name | HankelContourIntegral |

Date of creation | 2013-03-22 17:27:50 |

Last modified on | 2013-03-22 17:27:50 |

Owner | perucho (2192) |

Last modified by | perucho (2192) |

Numerical id | 5 |

Author | perucho (2192) |

Entry type | Result |

Classification | msc 30D30 |

Classification | msc 33B15 |