Fungrim entry: 3c662e

\left|U_{n}\!\left(x\right)\right| \le \left|n + 1\right|

Assumptions:

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \left[-1, 1\right]

TeX:

\left|U_{n}\!\left(x\right)\right| \le \left|n + 1\right|

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \left[-1, 1\right]

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`ChebyshevU`	$U_{n}\!\left(x\right)$	Chebyshev polynomial of the second kind
`ZZ`	$\mathbb{Z}$	Integers
`ClosedInterval`	$\left[a, b\right]$	Closed interval

Source code for this entry:

Entry(ID("3c662e"),
    Formula(LessEqual(Abs(ChebyshevU(n, x)), Abs(Add(n, 1)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, ClosedInterval(-1, 1)))))

Topics using this entry

Chebyshev 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