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Fungrim entry: 17eaad

BranchPoints⁡ ⁣(Wk ⁣(z),z,C∪{∞~})={0,−e−1,∞~}\operatorname{BranchPoints}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{0, -{e}^{-1}, {\tilde \infty}\right\}
Assumptions:k∈{−1,1}k \in \left\{-1, 1\right\}
TeX:
\operatorname{BranchPoints}\!\left(W_{k}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \left\{0, -{e}^{-1}, {\tilde \infty}\right\}

k \in \left\{-1, 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
Expez{e}^{z} Exponential function
Source code for this entry:
Entry(ID("17eaad"),
    Formula(Equal(BranchPoints(LambertW(k, z), z, Union(CC, Set(UnsignedInfinity))), Set(0, Neg(Exp(-1)), UnsignedInfinity))),
    Variables(k),
    Assumptions(Element(k, Set(-1, 1))))

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

2019-06-18 07:49:59.356594 UTC