# Fungrim entry: cce75b

$\lambda_{n} = \frac{1}{n} \sum_{\textstyle{k \in \mathbb{Z} \atop k \ne 0}} \left(1 - {\left(\frac{\rho_{k}}{\rho_{k} - 1}\right)}^{n}\right)$
Assumptions:$n \in \mathbb{Z}_{\ge 1}$
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
KeiperLiLambda$\lambda_{n}$ Keiper-Li coefficient
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
RiemannZetaZero$\rho_{n}$ Nontrivial zero of the Riemann zeta function
ZZ$\mathbb{Z}$ Integers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ 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))))

## 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