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Fungrim entry: 2caf78

HolomorphicDomain ⁣(Wk ⁣(z),z,C{~})=C(,0]\operatorname{HolomorphicDomain}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, 0\right]
Assumptions:kZ{0}k \in \mathbb{Z} \setminus \left\{0\right\}
TeX:
\operatorname{HolomorphicDomain}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, 0\right]

k \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
CCC\mathbb{C} Complex numbers
UnsignedInfinity~{\tilde \infty} Unsigned infinity
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("2caf78"),
    Formula(Equal(HolomorphicDomain(LambertW(k, z), z, Union(CC, Set(UnsignedInfinity))), SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))),
    Variables(k),
    Assumptions(Element(k, SetMinus(ZZ, Set(0)))))

Topics using this entry

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

2019-09-16 21:17:18.797188 UTC