# 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

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