Fungrim entry: f5c3c5

L\!\left(-n, \chi\right) = -\frac{B_{n + 1,\chi}}{n + 1}

Assumptions:

q \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
`DirichletL`	$L\!\left(s, \chi\right)$	Dirichlet L-function
`GeneralizedBernoulliB`	$B_{n,\chi}$	Generalized Bernoulli number
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`DirichletGroup`	$G_{q}$	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)))))

Topics using this entry

Dirichlet L-functions