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Fungrim entry: 0b3fd6

∣Un ⁣(z)∣≤∣Un ⁣(i∣z∣)∣\left|U_{n}\!\left(z\right)\right| \le \left|U_{n}\!\left(i \left|z\right|\right)\right|
Assumptions:n∈Z  and⁡  z∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
\left|U_{n}\!\left(z\right)\right| \le \left|U_{n}\!\left(i \left|z\right|\right)\right|

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
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
ConstIii Imaginary unit
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("0b3fd6"),
    Formula(LessEqual(Abs(ChebyshevU(n, z)), Abs(ChebyshevU(n, Mul(ConstI, Abs(z)))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZ), Element(z, CC))))

Topics using this entry

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