# hypergeometric equation

The hypergeometric equation is the following linear ordinary differential equation^{}:

$$x(1-x){y}^{\prime \prime}+(c-(a+b+1)x){y}^{\prime}-aby=0$$ |

(Here, $a$, $b$, and $c$ are complex constants.)

The solutions of this equation may be expressed in terms of the hypergeometric function^{}, hence the name.

The hypergeometric equation is a Fuchsian differential equation with singularities at $0$, $1$, and $\mathrm{\infty}$. By a suitable change of variables, any second order Fuchsian differential equation may be converted into a hypergeometric equation.

Title | hypergeometric equation |
---|---|

Canonical name | HypergeometricEquation |

Date of creation | 2013-03-22 14:45:53 |

Last modified on | 2013-03-22 14:45:53 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 6 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 33C05 |