Fungrim entry: 1e00d2

B_{n}^{2} \le B_{n - 1} B_{n + 1} \le \left(1 + \frac{1}{n}\right) B_{n}^{2}

Assumptions:

n \in \mathbb{Z}_{\ge 1}

References:

https://arxiv.org/abs/math/0104137

TeX:

B_{n}^{2} \le B_{n - 1} B_{n + 1} \le \left(1 + \frac{1}{n}\right) B_{n}^{2}

n \in \mathbb{Z}_{\ge 1}

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`BellNumber`	$B_{n}$	Bell number
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("1e00d2"),
    Formula(LessEqual(Pow(BellNumber(n), 2), Mul(BellNumber(Sub(n, 1)), BellNumber(Add(n, 1))), Mul(Add(1, Div(1, n)), Pow(BellNumber(n), 2)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))),
    References("https://arxiv.org/abs/math/0104137"))

Topics using this entry

Bell numbers

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

2021-03-15 19:12:00.328586 UTC