Fungrim entry: 58c19a

W_{0}\!\left(z\right) = \sum_{n=1}^{\infty} \frac{{\left(-n\right)}^{n - 1}}{n !} {z}^{n}

Assumptions:

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| \lt \frac{1}{e}

TeX:

W_{0}\!\left(z\right) = \sum_{n=1}^{\infty} \frac{{\left(-n\right)}^{n - 1}}{n !} {z}^{n}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| \lt \frac{1}{e}

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W_{k}\!\left(z\right)$	Lambert W-function
`Pow`	${a}^{b}$	Power
`Factorial`	$n !$	Factorial
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers
`Abs`	$\left\|z\right\|$	Absolute value
`ConstE`	$e$	The constant e (2.718...)

Source code for this entry:

Entry(ID("58c19a"),
    Formula(Equal(LambertW(0, z), Sum(Mul(Div(Pow(Neg(n), Sub(n, 1)), Factorial(n)), Pow(z, n)), Tuple(n, 1, Infinity)))),
    Variables(z),
    Assumptions(And(Element(z, CC), Less(Abs(z), Div(1, ConstE)))))

Topics using this entry

Lambert W-function

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

2019-06-18 07:49:59.356594 UTC