Fungrim entry: 382679

T_{n}\!\left(x\right) = \,{}_2F_1\!\left(-n, n, \frac{1}{2}, \frac{1 - x}{2}\right)

Assumptions:

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

TeX:

T_{n}\!\left(x\right) = \,{}_2F_1\!\left(-n, n, \frac{1}{2}, \frac{1 - x}{2}\right)

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
`Hypergeometric2F1`	$\,{}_2F_1\!\left(a, b, c, z\right)$	Gauss hypergeometric function
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("382679"),
    Formula(Equal(ChebyshevT(n, x), Hypergeometric2F1(Neg(n), n, Div(1, 2), Div(Sub(1, x), 2)))),
    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