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Fungrim entry: 448d90

ζ ⁣(s,a)=n=01(n+a)s\zeta\!\left(s, a\right) = \sum_{n=0}^{\infty} \frac{1}{{\left(n + a\right)}^{s}}
Assumptions:sC  and  Re(s)>1  and  aC{0,1,}s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1 \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\}
\zeta\!\left(s, a\right) = \sum_{n=0}^{\infty} \frac{1}{{\left(n + a\right)}^{s}}

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 1 \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\}
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
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(HurwitzZeta(s, a), Sum(Div(1, Pow(Add(n, a), s)), For(n, 0, Infinity)))),
    Variables(s, a),
    Assumptions(And(Element(s, CC), Greater(Re(s), 1), Element(a, SetMinus(CC, ZZLessEqual(0))))))

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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