# generalized Bernoulli number

Let $\chi $ be a non-trivial primitive character^{} mod $m$. The generalized Bernoulli numbers^{} ${B}_{n,\chi}$ are given by

$$\sum _{a=1}^{m}\chi (a)\frac{t{e}^{at}}{{e}^{mt}-1}=\sum _{n=0}^{\mathrm{\infty}}{B}_{n,\chi}\frac{{t}^{n}}{n!}$$ |

They are members of the field $\mathbb{Q}(\chi )$ generated by the values of $\chi $.

Title | generalized Bernoulli number |
---|---|

Canonical name | GeneralizedBernoulliNumber |

Date of creation | 2013-03-22 13:22:40 |

Last modified on | 2013-03-22 13:22:40 |

Owner | sucrose (1410) |

Last modified by | sucrose (1410) |

Numerical id | 6 |

Author | sucrose (1410) |

Entry type | Definition |

Classification | msc 11B68 |

Related topic | BernoulliNumber |