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Fungrim entry: ea271f

aC{0,1,}        (ζ ⁣(s,a) is meromorphic on sC)a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is meromorphic on } s \in \mathbb{C}\right)
a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is meromorphic on } s \in \mathbb{C}\right)
Fungrim symbol Notation Short description
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
IsMeromorphicf(z) is meromorphic at z=cf(z) \text{ is meromorphic at } z = c Meromorphic predicate
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Source code for this entry:
    Formula(Implies(Element(a, SetMinus(CC, ZZLessEqual(0))), IsMeromorphic(HurwitzZeta(s, a), ForElement(s, CC)))),

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2021-03-15 19:12:00.328586 UTC