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Fungrim entry: 4bf3da

(aC{0,1,})    (ζ ⁣(s,a) is holomorphic on sC{1})\left(a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } s \in \mathbb{C} \setminus \left\{1\right\}\right)
TeX:
\left(a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } s \in \mathbb{C} \setminus \left\{1\right\}\right)
Definitions:
Fungrim symbol Notation Short description
CCC\mathbb{C} Complex numbers
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
Source code for this entry:
Entry(ID("4bf3da"),
    Formula(Implies(Element(a, SetMinus(CC, ZZLessEqual(0))), IsHolomorphic(HurwitzZeta(s, a), ForElement(s, SetMinus(CC, Set(1)))))),
    Variables(a))

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2020-04-08 16:14:44.404316 UTC