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Fungrim entry: 88aeb6

Un ⁣(x)=(1)nUn ⁣(x)U_{n}\!\left(-x\right) = {\left(-1\right)}^{n} U_{n}\!\left(x\right)
Assumptions:nZandxCn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
U_{n}\!\left(-x\right) = {\left(-1\right)}^{n} U_{n}\!\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
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("88aeb6"),
    Formula(Equal(ChebyshevU(n, Neg(x)), Mul(Pow(-1, n), ChebyshevU(n, 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.

2019-09-22 15:43:45.410764 UTC