# Fungrim entry: 59e5df

$\left|P''_{n}(x)\right| \le \frac{\left(n - 1\right) n \left(n + 1\right) \left(n + 2\right)}{8}$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, -1 \le x \le 1$
TeX:
\left|P''_{n}(x)\right| \le \frac{\left(n - 1\right) n \left(n + 1\right) \left(n + 2\right)}{8}

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, -1 \le x \le 1
Definitions:
Fungrim symbol Notation Short description
Abs$\left|z\right|$ Absolute value
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
LegendrePolynomial$P_{n}\!\left(z\right)$ Legendre polynomial
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("59e5df"),
Formula(LessEqual(Abs(ComplexDerivative(LegendrePolynomial(n, x), For(x, x, 2))), Div(Mul(Mul(Mul(Sub(n, 1), n), Add(n, 1)), Add(n, 2)), 8))),
Variables(n, x),
Assumptions(And(Element(n, ZZGreaterEqual(0)), LessEqual(-1, x, 1))))

## Topics using this entry

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

2019-12-11 23:01:54.699850 UTC