Fungrim home page

Fungrim entry: 05c2dd

sZ2        (ζ ⁣(s,a) is meromorphic on aC)s \in \mathbb{Z}_{\ge 2} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is meromorphic on } a \in \mathbb{C}\right)
TeX:
s \in \mathbb{Z}_{\ge 2} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is meromorphic on } a \in \mathbb{C}\right)
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater 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
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("05c2dd"),
    Formula(Implies(Element(s, ZZGreaterEqual(2)), IsMeromorphic(HurwitzZeta(s, a), ForElement(a, CC)))),
    Variables(s))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC