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Fungrim entry: 9136b9

Wk ⁣(z)1zmax ⁣(3,1.5ez+1)\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1}{z}\right| \max\!\left(3, \left|\frac{1.5}{\sqrt{\left|e z + 1\right|}}\right|\right)
Assumptions:kZ  and  zCk \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
\left|W'_{k}\!\left(z\right)\right| \le \left|\frac{1}{z}\right| \max\!\left(3, \left|\frac{1.5}{\sqrt{\left|e z + 1\right|}}\right|\right)

k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
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...)
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(LessEqual(Abs(LambertW(z, k, 1)), Mul(Abs(Div(1, z)), Max(3, Abs(Div(Decimal("1.5"), Sqrt(Abs(Add(Mul(ConstE, z), 1))))))))),
    Variables(k, z),
    Assumptions(And(Element(k, ZZ), Element(z, CC))))

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2021-03-15 19:12:00.328586 UTC