Fungrim entry: 0bd6aa

\zeta\!\left(s, N\right) = \sum_{n=N}^{\infty} \frac{1}{{n}^{s}}

Assumptions:

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1 \;\mathbin{\operatorname{and}}\; N \in \mathbb{Z}_{\ge 1}

TeX:

\zeta\!\left(s, N\right) = \sum_{n=N}^{\infty} \frac{1}{{n}^{s}}

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1 \;\mathbin{\operatorname{and}}\; N \in \mathbb{Z}_{\ge 1}

Definitions:

Fungrim symbol	Notation	Short description
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers
`Re`	$\operatorname{Re}(z)$	Real part
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("0bd6aa"),
    Formula(Equal(HurwitzZeta(s, N), Sum(Div(1, Pow(n, s)), For(n, N, Infinity)))),
    Variables(s, N),
    Assumptions(And(Element(s, CC), Greater(Re(s), 1), Element(N, ZZGreaterEqual(1)))))

Topics using this entry

Hurwitz zeta function