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Fungrim entry: b3d435

∣Wk′ ⁣(z)∣≤∣1.2z∣\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1.2}{z}\right|
Assumptions:k∈Z∖{−1,0,1}  and⁡  z∈Ck \in \mathbb{Z} \setminus \left\{-1, 0, 1\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1.2}{z}\right|

k \in \mathbb{Z} \setminus \left\{-1, 0, 1\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("b3d435"),
    Formula(LessEqual(Abs(LambertW(z, k, 1)), Abs(Div(Decimal("1.2"), z)))),
    Variables(k, z),
    Assumptions(And(Element(k, SetMinus(ZZ, Set(-1, 0, 1))), Element(z, CC))))

Topics using this entry

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

2021-03-15 19:12:00.328586 UTC