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Fungrim entry: 589758

Bn∼n−1/2(nW ⁣(n))n+1/2exp⁡ ⁣(nW ⁣(n)−n−1),  n→∞B_{n} \sim {n}^{-1 / 2} {\left(\frac{n}{W\!\left(n\right)}\right)}^{n + 1 / 2} \exp\!\left(\frac{n}{W\!\left(n\right)} - n - 1\right), \; n \to \infty
TeX:
B_{n} \sim {n}^{-1 / 2} {\left(\frac{n}{W\!\left(n\right)}\right)}^{n + 1 / 2} \exp\!\left(\frac{n}{W\!\left(n\right)} - n - 1\right), \; n \to \infty
Definitions:
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
Powab{a}^{b} Power
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
Expez{e}^{z} Exponential function
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("589758"),
    Formula(AsymptoticTo(BellNumber(n), Mul(Mul(Pow(n, Neg(Div(1, 2))), Pow(Div(n, LambertW(n)), Add(n, Div(1, 2)))), Exp(Sub(Sub(Div(n, LambertW(n)), n), 1))), n, Infinity)))

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2021-03-15 19:12:00.328586 UTC