Fungrim home page

Fungrim entry: d1ef91

Un ⁣(x)=2xUn1 ⁣(x)Un2 ⁣(x)U_{n}\!\left(x\right) = 2 x U_{n - 1}\!\left(x\right) - U_{n - 2}\!\left(x\right)
Assumptions:nZ  and  xCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
U_{n}\!\left(x\right) = 2 x U_{n - 1}\!\left(x\right) - U_{n - 2}\!\left(x\right)

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Fungrim symbol Notation Short description
ChebyshevUUn ⁣(x)U_{n}\!\left(x\right) Chebyshev polynomial of the second kind
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(ChebyshevU(n, x), Sub(Mul(Mul(2, x), ChebyshevU(Sub(n, 1), x)), ChebyshevU(Sub(n, 2), x)))),
    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.

2021-03-15 19:12:00.328586 UTC