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Fungrim entry: cce75b

λn=1nkZk0(1(ρkρk1)n)\lambda_{n} = \frac{1}{n} \sum_{\textstyle{k \in \mathbb{Z} \atop k \ne 0}} \left(1 - {\left(\frac{\rho_{k}}{\rho_{k} - 1}\right)}^{n}\right)
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
TeX:
\lambda_{n} = \frac{1}{n} \sum_{\textstyle{k \in \mathbb{Z} \atop k \ne 0}} \left(1 - {\left(\frac{\rho_{k}}{\rho_{k} - 1}\right)}^{n}\right)

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
KeiperLiLambdaλn\lambda_{n} Keiper-Li coefficient
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
RiemannZetaZeroρn\rho_{n} Nontrivial zero of the Riemann zeta function
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("cce75b"),
    Formula(Equal(KeiperLiLambda(n), Mul(Div(1, n), Sum(Parentheses(Sub(1, Pow(Div(RiemannZetaZero(k), Sub(RiemannZetaZero(k), 1)), n))), ForElement(k, ZZ), NotEqual(k, 0))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC