Fungrim entry: 9136b9

\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1}{z}\right| \max\!\left(3, \left|\frac{1.5}{\sqrt{\left|e z + 1\right|}}\right|\right)

Assumptions:

k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

TeX:

\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1}{z}\right| \max\!\left(3, \left|\frac{1.5}{\sqrt{\left|e z + 1\right|}}\right|\right)

k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`Sqrt`	$\sqrt{z}$	Principal square root
`ConstE`	$e$	The constant e (2.718...)
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("9136b9"),
    Formula(LessEqual(Abs(LambertW(z, k, 1)), Mul(Abs(Div(1, z)), Max(3, Abs(Div(Decimal("1.5"), Sqrt(Abs(Add(Mul(ConstE, z), 1))))))))),
    Variables(k, z),
    Assumptions(And(Element(k, ZZ), Element(z, CC))))

Topics using this entry

Lambert W-function