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Fungrim entry: f045b3

(s{0,1,})    (ζ ⁣(s,a) is holomorphic on aC)\left(s \in \{0, -1, \ldots\}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C}\right)
TeX:
\left(s \in \{0, -1, \ldots\}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C}\right)
Definitions:
Fungrim symbol Notation Short description
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less 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
Source code for this entry:
Entry(ID("f045b3"),
    Formula(Implies(Element(s, ZZLessEqual(0)), IsHolomorphic(HurwitzZeta(s, a), ForElement(a, CC)))),
    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