Fungrim entry: b786ad

\left|P'_{n}(x)\right| \le \frac{n \left(n + 1\right)}{2}

Assumptions:

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; -1 \le x \le 1

TeX:

\left|P'_{n}(x)\right| \le \frac{n \left(n + 1\right)}{2}

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("b786ad"),
    Formula(LessEqual(Abs(ComplexDerivative(LegendrePolynomial(n, x), For(x, x, 1))), Div(Mul(n, Add(n, 1)), 2))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), LessEqual(-1, x, 1))))

Topics using this entry

Legendre polynomials

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