# Fungrim entry: 8e06be

$\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1.5}{z}\right|$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left(\left(k = 1 \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) \ge 0\right) \,\mathbin{\operatorname{or}}\, \left(k = -1 \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) < 0\right)\right)$
TeX:
\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1.5}{z}\right|

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left(\left(k = 1 \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) \ge 0\right) \,\mathbin{\operatorname{or}}\, \left(k = -1 \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) < 0\right)\right)
Definitions:
Fungrim symbol Notation Short description
Abs$\left|z\right|$ Absolute value
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
CC$\mathbb{C}$ Complex numbers
Im$\operatorname{Im}(z)$ Imaginary part
Source code for this entry:
Entry(ID("8e06be"),
Formula(LessEqual(Abs(LambertW(k, z, 1)), Abs(Div(Decimal("1.5"), z)))),
Variables(k, z),
Assumptions(And(Element(z, CC), Or(And(Equal(k, 1), GreaterEqual(Im(z), 0)), And(Equal(k, -1), Less(Im(z), 0))))))

## Topics using this entry

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