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Fungrim entry: 26418b

(aC)    (ζ ⁣(s,a) is holomorphic on s{t:tCandRe(t)<0})\left(a \in \mathbb{C}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } s \in \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(t) < 0 \right\}\right)
TeX:
\left(a \in \mathbb{C}\right) \implies \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } s \in \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(t) < 0 \right\}\right)
Definitions:
Fungrim symbol Notation Short description
CCC\mathbb{C} Complex numbers
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
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
Entry(ID("26418b"),
    Formula(Implies(Element(a, CC), IsHolomorphic(HurwitzZeta(s, a), ForElement(s, Set(t, ForElement(t, CC), Less(Re(t), 0)))))),
    Variables(a))

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2020-04-08 16:14:44.404316 UTC