# abelian function

An abelian or hyperelliptic function is a generalisation of an elliptic function^{}. It is a function of two variables with four periods.
In a similar way to an elliptic function it can also be regarded as the inverse function^{} to certain integrals^{} (called abelian or hyperelliptic integrals) of the form

$$\int \frac{dz}{R(z)}$$ |

where $R$ is a polynomial of degree greater than 4.

Title | abelian function |
---|---|

Canonical name | AbelianFunction |

Date of creation | 2013-03-22 14:43:34 |

Last modified on | 2013-03-22 14:43:34 |

Owner | vmoraru (1243) |

Last modified by | vmoraru (1243) |

Numerical id | 5 |

Author | vmoraru (1243) |

Entry type | Definition |

Classification | msc 26-00 |

Synonym | hyperelliptic function |