Fungrim entry: 58c19a

W\!\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| < \frac{1}{e}

TeX:

W\!\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| < \frac{1}{e}

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`Sum`	$\sum_{n} f(n)$	Sum
`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(z), Sum(Mul(Div(Pow(Neg(n), Sub(n, 1)), Factorial(n)), Pow(z, n)), For(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.

2021-03-15 19:12:00.328586 UTC