# hypergeometric function

Let $(a,b,c)$ be a triple of complex numbers with $c$ not belonging to the set of negative integers. For a complex number $w$ and a non negative integer $n$, use Pochhammer symbol^{} ${(w)}_{n}$ , to denote the expression :

$${(w)}_{n}=w(w+1)\mathrm{\dots}(w+n-1).$$ |

The *Gauss hypergeometric function*, ${}_{2}F_{1}$, is then defined by the following power series expansion :

$${}_{2}F_{1}(a,b;c;z)=\sum _{n=0}^{\mathrm{\infty}}\frac{{(a)}_{n}{(b)}_{n}}{{(c)}_{n}n!}{z}^{n}.$$ |

Title | hypergeometric function^{} |
---|---|

Canonical name | HypergeometricFunction |

Date of creation | 2013-03-22 14:27:48 |

Last modified on | 2013-03-22 14:27:48 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 9 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 33C05 |

Related topic | TableOfMittagLefflerPartialFractionExpansions |

Defines | Gauss hypergeometric function |