# Fungrim entry: 9697b8

$\log\!\left(g(n)\right) \le \sqrt{n \log(n)} \left(1 + \frac{\log\!\left(\log(n)\right) - 0.975}{2 \log(n)}\right)$
Assumptions:$n \in \mathbb{Z}_{\ge 4}$
References:
• Jean-Pierre Massias, Jean-Louis Nicolas and Guy Robin (1989), Effective bounds for the maximal order of an element in the symmetric group, Mathematics of Computation, 53, 118, 665--665, https://doi.org/10.1090/s0025-5718-1989-0979940-4
TeX:
\log\!\left(g(n)\right) \le \sqrt{n \log(n)} \left(1 + \frac{\log\!\left(\log(n)\right) - 0.975}{2 \log(n)}\right)

n \in \mathbb{Z}_{\ge 4}
Definitions:
Fungrim symbol Notation Short description
Log$\log(z)$ Natural logarithm
LandauG$g(n)$ Landau's function
Sqrt$\sqrt{z}$ Principal square root
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("9697b8"),
Formula(LessEqual(Log(LandauG(n)), Mul(Sqrt(Mul(n, Log(n))), Add(1, Div(Sub(Log(Log(n)), Decimal("0.975")), Mul(2, Log(n))))))),
Variables(n),
Assumptions(Element(n, ZZGreaterEqual(4))),
References("Jean-Pierre Massias, Jean-Louis Nicolas and Guy Robin (1989), Effective bounds for the maximal order of an element in the symmetric group, Mathematics of Computation, 53, 118, 665--665, https://doi.org/10.1090/s0025-5718-1989-0979940-4"))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC