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Fungrim entry: e50532

W0 ⁣(z)=n=0μnvn   where v=2(ez+1)W_{0}\!\left(z\right) = \sum_{n=0}^{\infty} \mu_{n} {v}^{n}\; \text{ where } v = \sqrt{2 \left(e z + 1\right)}
Assumptions:zCandez+1<1z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|e z + 1\right| < 1
TeX:
W_{0}\!\left(z\right) = \sum_{n=0}^{\infty} \mu_{n} {v}^{n}\; \text{ where } v = \sqrt{2 \left(e z + 1\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|e z + 1\right| < 1
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
LambertWPuiseuxCoefficientμk\mu_{k} Coefficient in scaled Puiseux expansion of Lambert W-function
Powab{a}^{b} Power
Infinity\infty Positive infinity
Sqrtz\sqrt{z} Principal square root
ConstEee The constant e (2.718...)
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
Entry(ID("e50532"),
    Formula(Where(Equal(LambertW(0, z), Sum(Mul(LambertWPuiseuxCoefficient(n), Pow(v, n)), Tuple(n, 0, Infinity))), Equal(v, Sqrt(Mul(2, Add(Mul(ConstE, z), 1)))))),
    Variables(z),
    Assumptions(And(Element(z, CC), Less(Abs(Add(Mul(ConstE, z), 1)), 1))))

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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 14:14:26.267625 UTC