Fungrim entry: b8fdcd

U_{n - 1}\!\left(x\right) \sqrt{1 - {x}^{2}} = \sin\!\left(n \operatorname{acos}(x)\right)

Assumptions:

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}

TeX:

U_{n - 1}\!\left(x\right) \sqrt{1 - {x}^{2}} = \sin\!\left(n \operatorname{acos}(x)\right)

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`ChebyshevU`	$U_{n}\!\left(x\right)$	Chebyshev polynomial of the second kind
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Sin`	$\sin(z)$	Sine
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("b8fdcd"),
    Formula(Equal(Mul(ChebyshevU(Sub(n, 1), x), Sqrt(Sub(1, Pow(x, 2)))), Sin(Mul(n, Acos(x))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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