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Fungrim entry: 343946

log⁡ ⁣(Bn)n∼log⁡(n)−log⁡ ⁣(log⁡(n))−1+log⁡ ⁣(log⁡(n))log⁡(n)+1log⁡(n)+12(log⁡ ⁣(log⁡(n))log⁡(n))2,  n→∞\frac{\log\!\left(B_{n}\right)}{n} \sim \log(n) - \log\!\left(\log(n)\right) - 1 + \frac{\log\!\left(\log(n)\right)}{\log(n)} + \frac{1}{\log(n)} + \frac{1}{2} {\left(\frac{\log\!\left(\log(n)\right)}{\log(n)}\right)}^{2}, \; n \to \infty
TeX:
\frac{\log\!\left(B_{n}\right)}{n} \sim \log(n) - \log\!\left(\log(n)\right) - 1 + \frac{\log\!\left(\log(n)\right)}{\log(n)} + \frac{1}{\log(n)} + \frac{1}{2} {\left(\frac{\log\!\left(\log(n)\right)}{\log(n)}\right)}^{2}, \; n \to \infty
Definitions:
Fungrim symbol Notation Short description
Loglog⁡(z)\log(z) Natural logarithm
BellNumberBnB_{n} Bell number
Powab{a}^{b} Power
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("343946"),
    Formula(AsymptoticTo(Div(Log(BellNumber(n)), n), Add(Add(Add(Sub(Sub(Log(n), Log(Log(n))), 1), Div(Log(Log(n)), Log(n))), Div(1, Log(n))), Mul(Div(1, 2), Pow(Div(Log(Log(n)), Log(n)), 2))), n, Infinity)))

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2021-03-15 19:12:00.328586 UTC