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Fungrim entry: 0eb699

W0 ⁣(z)2.25t(1+t)   where t=ez+1\left|W'_{0}\!\left(z\right)\right| \le \left|\frac{2.25}{\sqrt{t \left(1 + t\right)}}\right|\; \text{ where } t = \left|e z + 1\right|
Assumptions:zC  and  z64z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \le 64
\left|W'_{0}\!\left(z\right)\right| \le \left|\frac{2.25}{\sqrt{t \left(1 + t\right)}}\right|\; \text{ where } t = \left|e z + 1\right|

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \le 64
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
Sqrtz\sqrt{z} Principal square root
ConstEee The constant e (2.718...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Where(LessEqual(Abs(LambertW(z, 0, 1)), Abs(Div(Decimal("2.25"), Sqrt(Mul(t, Add(1, t)))))), Equal(t, Abs(Add(Mul(ConstE, z), 1))))),
    Assumptions(And(Element(z, CC), LessEqual(Abs(z), 64))))

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2021-03-15 19:12:00.328586 UTC