Fungrim entry: 88aeb6

U_{n}\!\left(-x\right) = {\left(-1\right)}^{n} U_{n}\!\left(x\right)

Assumptions:

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

TeX:

U_{n}\!\left(-x\right) = {\left(-1\right)}^{n} U_{n}\!\left(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
`Pow`	${a}^{b}$	Power
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("88aeb6"),
    Formula(Equal(ChebyshevU(n, Neg(x)), Mul(Pow(-1, n), ChebyshevU(n, 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.

2019-06-18 07:49:59.356594 UTC