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Fungrim entry: 78f5bb

U−n ⁣(x)=−Un−2 ⁣(x)U_{-n}\!\left(x\right) = -U_{n - 2}\!\left(x\right)
Assumptions:n∈Z and⁡ x∈Cn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
U_{-n}\!\left(x\right) = -U_{n - 2}\!\left(x\right)

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
Definitions:
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:
Entry(ID("78f5bb"),
    Formula(Equal(ChebyshevU(Neg(n), x), Neg(ChebyshevU(Sub(n, 2), x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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

2019-06-18 07:49:59.356594 UTC