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Fungrim entry: 58c19a

W ⁣(z)=n=1(n)n1n!znW\!\left(z\right) = \sum_{n=1}^{\infty} \frac{{\left(-n\right)}^{n - 1}}{n !} {z}^{n}
Assumptions:zC  and  z<1ez \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < \frac{1}{e}
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}
Fungrim symbol Notation Short description
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
Sumnf(n)\sum_{n} f(n) 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:
    Formula(Equal(LambertW(z), Sum(Mul(Div(Pow(Neg(n), Sub(n, 1)), Factorial(n)), Pow(z, n)), For(n, 1, Infinity)))),
    Assumptions(And(Element(z, CC), Less(Abs(z), Div(1, ConstE)))))

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2021-03-15 19:12:00.328586 UTC