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Fungrim entry: 72712c

Wk ⁣(z)1z\left|W'_{k}\!\left(z\right)\right| \le \frac{1}{\left|z\right|}
Assumptions:(k=0  and  z1)  or  (kZ  and  zC  and  z4(k+1))\left(k = 0 \;\mathbin{\operatorname{and}}\; \left|z\right| \ge 1\right) \;\mathbin{\operatorname{or}}\; \left(k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \ge 4 \left(\left|k\right| + 1\right)\right)
\left|W'_{k}\!\left(z\right)\right| \le \frac{1}{\left|z\right|}

\left(k = 0 \;\mathbin{\operatorname{and}}\; \left|z\right| \ge 1\right) \;\mathbin{\operatorname{or}}\; \left(k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| \ge 4 \left(\left|k\right| + 1\right)\right)
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(LessEqual(Abs(LambertW(z, k, 1)), Div(1, Abs(z)))),
    Variables(k, z),
    Assumptions(Or(And(Equal(k, 0), GreaterEqual(Abs(z), 1)), And(Element(k, ZZ), Element(z, CC), GreaterEqual(Abs(z), Mul(4, Add(Abs(k), 1)))))))

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2021-03-15 19:12:00.328586 UTC