Fungrim home page

# Fungrim entry: 5f09f4

$U_{2 n}\!\left(x\right) = T_{n}\!\left(2 {x}^{2} - 1\right) + U_{n - 1}\!\left(2 {x}^{2} - 1\right)$
Assumptions:$n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}$
TeX:
U_{2 n}\!\left(x\right) = T_{n}\!\left(2 {x}^{2} - 1\right) + U_{n - 1}\!\left(2 {x}^{2} - 1\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
Pow${a}^{b}$ Power
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("5f09f4"),
Formula(Equal(ChebyshevU(Mul(2, n), x), Add(ChebyshevT(n, Sub(Mul(2, Pow(x, 2)), 1)), ChebyshevU(Sub(n, 1), Sub(Mul(2, Pow(x, 2)), 1))))),
Variables(n, x),
Assumptions(And(Element(n, ZZ), Element(x, CC))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC