Fungrim entry: ce5e03

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

Assumptions:

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

TeX:

U_{n}\!\left(x\right) = x U_{n - 1}\!\left(x\right) + T_{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
`ChebyshevT`	$T_{n}\!\left(x\right)$	Chebyshev polynomial of the first kind
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("ce5e03"),
    Formula(Equal(ChebyshevU(n, x), Add(Mul(x, ChebyshevU(Sub(n, 1), x)), ChebyshevT(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.

2021-03-15 19:12:00.328586 UTC