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Fungrim entry: 3c662e

∣Un ⁣(x)∣≤∣n+1∣\left|U_{n}\!\left(x\right)\right| \le \left|n + 1\right|
Assumptions:n∈Z and⁡ x∈[−1,1]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∣z∣\left|z\right| Absolute value
ChebyshevUUn ⁣(x)U_{n}\!\left(x\right) Chebyshev polynomial of the second kind
ZZZ\mathbb{Z} Integers
ClosedInterval[a,b]\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

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