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Fungrim entry: 44ad09

{W ⁣(x):x(,e1)}={ycot(y)+yi:y(0,π)}\left\{ W\!\left(x\right) : x \in \left(-\infty, -{e}^{-1}\right) \right\} = \left\{ -y \cot(y) + y i : y \in \left(0, \pi\right) \right\}
\left\{ W\!\left(x\right) : x \in \left(-\infty, -{e}^{-1}\right) \right\} = \left\{ -y \cot(y) + y i : y \in \left(0, \pi\right) \right\}
Fungrim symbol Notation Short description
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
Piπ\pi The constant pi (3.14...)
Source code for this entry:
    Formula(Equal(Set(LambertW(x), ForElement(x, OpenInterval(Neg(Infinity), Neg(Exp(-1))))), Set(Add(Mul(Neg(y), Cot(y)), Mul(y, ConstI)), ForElement(y, OpenInterval(0, Pi))))))

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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