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Fungrim entry: 6e69fc

ζ ⁣(s,n)=ζ ⁣(s)k=1n11ks\zeta\!\left(s, n\right) = \zeta\!\left(s\right) - \sum_{k=1}^{n - 1} \frac{1}{{k}^{s}}
Assumptions:sC  and  nZ1s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
\zeta\!\left(s, n\right) = \zeta\!\left(s\right) - \sum_{k=1}^{n - 1} \frac{1}{{k}^{s}}

s \in \mathbb{C} \;\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
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(HurwitzZeta(s, n), Sub(RiemannZeta(s), Sum(Div(1, Pow(k, s)), For(k, 1, Sub(n, 1)))))),
    Variables(s, n),
    Assumptions(And(Element(s, CC), Element(n, ZZGreaterEqual(1)))))

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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