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Fungrim entry: 58c19a

W0 ⁣(z)=n=1(n)n1n!znW_{0}\!\left(z\right) = \sum_{n=1}^{\infty} \frac{{\left(-n\right)}^{n - 1}}{n !} {z}^{n}
Assumptions:zCandz<1ez \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < \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| < \frac{1}{e}
Definitions:
Fungrim symbol Notation Short description
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
ConstEee 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)))))

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

2019-09-15 13:58:57.282983 UTC