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Fungrim entry: 56dcbd

(sC{1}  and  aC{0,1,})        ζ ⁣(s,a)C\left(s \in \mathbb{C} \setminus \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{C}
TeX:
\left(s \in \mathbb{C} \setminus \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Source code for this entry:
Entry(ID("56dcbd"),
    Formula(Implies(And(Element(s, SetMinus(CC, Set(1))), Element(a, SetMinus(CC, ZZLessEqual(0)))), Element(HurwitzZeta(s, a), CC))),
    Variables(s, a))

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2021-03-15 19:12:00.328586 UTC