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Fungrim entry: 2caf78

Wk ⁣(z) is holomorphic on zC(,0]W_{k}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \left(-\infty, 0\right]
Assumptions:kZ{0}k \in \mathbb{Z} \setminus \left\{0\right\}
TeX:
W_{k}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \left(-\infty, 0\right]

k \in \mathbb{Z} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
CCC\mathbb{C} Complex numbers
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(IsHolomorphic(LambertW(k, z), ForElement(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))),
    Variables(k),
    Assumptions(Element(k, SetMinus(ZZ, Set(0)))))

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

2020-01-31 18:09:28.494564 UTC