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Fungrim entry: 0bd6aa

ζ ⁣(s,N)=n=N1ns\zeta\!\left(s, N\right) = \sum_{n=N}^{\infty} \frac{1}{{n}^{s}}
Assumptions:sC  and  Re(s)>1  and  NZ1s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1 \;\mathbin{\operatorname{and}}\; N \in \mathbb{Z}_{\ge 1}
\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}
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    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)))))

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2021-03-15 19:12:00.328586 UTC