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Fungrim entry: 0d3b91

HolomorphicDomain ⁣(W0 ⁣(z),z,C{~})=C(,e1]\operatorname{HolomorphicDomain}\!\left(W_{0}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, -{e}^{-1}\right]
TeX:
\operatorname{HolomorphicDomain}\!\left(W_{0}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, -{e}^{-1}\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
Expez{e}^{z} Exponential function
Source code for this entry:
Entry(ID("0d3b91"),
    Formula(Equal(HolomorphicDomain(LambertW(0, z), z, Union(CC, Set(UnsignedInfinity))), SetMinus(CC, OpenClosedInterval(Neg(Infinity), Neg(Exp(-1)))))))

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