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Fungrim entry: f7a866

B0,χ={φ(q)q,χ=χq.10,otherwiseB_{0,\chi} = \begin{cases} \frac{\varphi(q)}{q}, & \chi = \chi_{q \, . \, 1}\\0, & \text{otherwise}\\ \end{cases}
Assumptions:qZ1  and  χGqq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}
B_{0,\chi} = \begin{cases} \frac{\varphi(q)}{q}, & \chi = \chi_{q \, . \, 1}\\0, & \text{otherwise}\\ \end{cases}

q \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q}
Fungrim symbol Notation Short description
GeneralizedBernoulliBBn,χB_{n,\chi} Generalized Bernoulli number
Totientφ(n)\varphi(n) Euler totient function
DirichletCharacterχq.\chi_{q \, . \, \ell} Dirichlet character
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(GeneralizedBernoulliB(0, chi), Cases(Tuple(Div(Totient(q), q), Equal(chi, DirichletCharacter(q, 1))), Tuple(0, Otherwise)))),
    Variables(q, chi),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)))))

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2020-04-08 16:14:44.404316 UTC