Fungrim entry: 0eb699

\left|W'_{0}\!\left(z\right)\right| \le \left|\frac{2.25}{\sqrt{t \left(1 + t\right)}}\right|\; \text{ where } t = \left|e z + 1\right|

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \le 64

TeX:

\left|W'_{0}\!\left(z\right)\right| \le \left|\frac{2.25}{\sqrt{t \left(1 + t\right)}}\right|\; \text{ where } t = \left|e z + 1\right|

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \le 64

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...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("0eb699"),
    Formula(Where(LessEqual(Abs(LambertW(z, 0, 1)), Abs(Div(Decimal("2.25"), Sqrt(Mul(t, Add(1, t)))))), Equal(t, Abs(Add(Mul(ConstE, z), 1))))),
    Variables(z),
    Assumptions(And(Element(z, CC), LessEqual(Abs(z), 64))))

Topics using this entry

Lambert W-function