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Fungrim entry: b786ad

∣ddx Pn ⁣(x)∣≤n(n+1)2\left|\frac{d}{d x}\, P_{n}\!\left(x\right)\right| \le \frac{n \left(n + 1\right)}{2}
Assumptions:n∈Z≥0 and⁡ −1≤x≤1n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, -1 \le x \le 1
TeX:
\left|\frac{d}{d x}\, P_{n}\!\left(x\right)\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∣z∣\left|z\right| Absolute value
Derivativeddz f ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("b786ad"),
    Formula(LessEqual(Abs(Derivative(LegendrePolynomial(n, x), Tuple(x, x, 1))), Div(Mul(n, Add(n, 1)), 2))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), LessEqual(-1, x, 1))))

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

2019-06-18 07:49:59.356594 UTC