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Fungrim entry: f5c3c5

L ⁣(n,χ)=Bn+1,χn+1L\!\left(-n, \chi\right) = -\frac{B_{n + 1,\chi}}{n + 1}
Assumptions:qZ1andχGqandnZ0q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
TeX:
L\!\left(-n, \chi\right) = -\frac{B_{n + 1,\chi}}{n + 1}

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
DirichletLL ⁣(s,χ)L\!\left(s, \chi\right) Dirichlet L-function
GeneralizedBernoulliBBn,χB_{n,\chi} Generalized Bernoulli number
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
Source code for this entry:
Entry(ID("f5c3c5"),
    Formula(Equal(DirichletL(Neg(n), chi), Neg(Div(GeneralizedBernoulliB(Add(n, 1), chi), Add(n, 1))))),
    Variables(q, chi, n),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)), Element(n, ZZGreaterEqual(0)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC