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Fungrim entry: b8fdcd

Un1 ⁣(x)1x2=sin ⁣(nacos(x))U_{n - 1}\!\left(x\right) \sqrt{1 - {x}^{2}} = \sin\!\left(n \operatorname{acos}(x)\right)
Assumptions:nZ  and  xCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
U_{n - 1}\!\left(x\right) \sqrt{1 - {x}^{2}} = \sin\!\left(n \operatorname{acos}(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
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Mul(ChebyshevU(Sub(n, 1), x), Sqrt(Sub(1, Pow(x, 2)))), Sin(Mul(n, Acos(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.

2021-03-15 19:12:00.328586 UTC