# Fungrim entry: fcab61

$\lambda_{n} = \frac{1}{n !} \left[ \frac{d^{n}}{{d s}^{n}} \log\!\left(2 \xi\!\left(\frac{s}{s - 1}\right)\right) \right]_{s = 0}$
Assumptions:$n \in \mathbb{Z}_{\ge 0}$
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
KeiperLiLambda$\lambda_{n}$ Keiper-Li coefficient
Factorial$n !$ Factorial
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
Log$\log(z)$ Natural logarithm
RiemannXi$\xi(s)$ Riemann xi-function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ 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))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC