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Fungrim entry: 1ba9a5

∣Pn ⁣(x)∣≤1\left|P_{n}\!\left(x\right)\right| \le 1
Assumptions:n∈Z≥0  and⁡  −1≤x≤1n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; -1 \le x \le 1
TeX:
\left|P_{n}\!\left(x\right)\right| \le 1

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
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("1ba9a5"),
    Formula(LessEqual(Abs(LegendrePolynomial(n, x)), 1)),
    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.

2021-03-15 19:12:00.328586 UTC