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Fungrim entry: 8c7cdb

(sZ2)    (ζ ⁣(s,a) is holomorphic on aC{0,1,})\left(s \in \mathbb{Z}_{\ge 2}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right)
TeX:
\left(s \in \mathbb{Z}_{\ge 2}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right)
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("8c7cdb"),
    Formula(Implies(Element(s, ZZGreaterEqual(2)), IsHolomorphic(HurwitzZeta(s, a), ForElement(a, SetMinus(CC, ZZLessEqual(0)))))),
    Variables(s))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC