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Fungrim entry: fcab61

λn=1n![dndsnlog⁡ ⁣(2ξ ⁣(ss−1))]s=0\lambda_{n} = \frac{1}{n !} \left[ \frac{d^{n}}{{d s}^{n}} \log\!\left(2 \xi\!\left(\frac{s}{s - 1}\right)\right) \right]_{s = 0}
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
\lambda_{n} = \frac{1}{n !} \left[ \frac{d^{n}}{{d s}^{n}} \log\!\left(2 \xi\!\left(\frac{s}{s - 1}\right)\right) \right]_{s = 0}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
KeiperLiLambdaλn\lambda_{n} Keiper-Li coefficient
Factorialn!n ! Factorial
ComplexDerivativeddz f ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Loglog⁡(z)\log(z) Natural logarithm
RiemannXiξ(s)\xi(s) Riemann xi-function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("fcab61"),
    Formula(Equal(KeiperLiLambda(n), Mul(Div(1, Factorial(n)), ComplexDerivative(Log(Mul(2, RiemannXi(Div(s, Sub(s, 1))))), For(s, 0, n))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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2021-03-15 19:12:00.328586 UTC