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Fungrim entry: 26418b

aC        (ζ ⁣(s,a) is holomorphic on s{t:tCandRe(t)<0})a \in \mathbb{C} \;\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)
a \in \mathbb{C} \;\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)
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:
    Formula(Implies(Element(a, CC), IsHolomorphic(HurwitzZeta(s, a), ForElement(s, Set(t, ForElement(t, CC), Less(Re(t), 0)))))),

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2021-03-15 19:12:00.328586 UTC