Fungrim entry: 4b83c6

T_{2 n}\!\left(x\right) = 2 T_{n}^{2}\!\left(x\right) - 1

Assumptions:

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

TeX:

T_{2 n}\!\left(x\right) = 2 T_{n}^{2}\!\left(x\right) - 1

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

Definitions:

Fungrim symbol	Notation	Short description
`ChebyshevT`	$T_{n}\!\left(x\right)$	Chebyshev polynomial of the first kind
`Pow`	${a}^{b}$	Power
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("4b83c6"),
    Formula(Equal(ChebyshevT(Mul(2, n), x), Sub(Mul(2, Pow(ChebyshevT(n, x), 2)), 1))),
    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