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Fungrim entry: 844561

Tn ⁣(x)=Un ⁣(x)xUn1 ⁣(x)T_{n}\!\left(x\right) = U_{n}\!\left(x\right) - x U_{n - 1}\!\left(x\right)
Assumptions:nZandxCn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
T_{n}\!\left(x\right) = U_{n}\!\left(x\right) - x U_{n - 1}\!\left(x\right)

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
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("844561"),
    Formula(Equal(ChebyshevT(n, x), Sub(ChebyshevU(n, x), Mul(x, ChebyshevU(Sub(n, 1), x))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2019-10-05 13:11:19.856591 UTC