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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:qZ1  and  χGq  and  nZ0q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
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}
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:
    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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2021-03-15 19:12:00.328586 UTC