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

Keiper-Li coefficients