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Fungrim entry: f045b3

s{0,1,}        (ζ ⁣(s,a) is holomorphic on aC)s \in \{0, -1, \ldots\} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C}\right)
s \in \{0, -1, \ldots\} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C}\right)
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:
    Formula(Implies(Element(s, ZZLessEqual(0)), IsHolomorphic(HurwitzZeta(s, a), ForElement(a, CC)))),

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2021-03-15 19:12:00.328586 UTC