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Fungrim entry: 7b2c26

Tn ⁣(x)=xTn−1 ⁣(x)−(1−x2)Un−2 ⁣(x)T_{n}\!\left(x\right) = x T_{n - 1}\!\left(x\right) - \left(1 - {x}^{2}\right) U_{n - 2}\!\left(x\right)
Assumptions:n∈Z  and⁡  x∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{n}\!\left(x\right) = x T_{n - 1}\!\left(x\right) - \left(1 - {x}^{2}\right) U_{n - 2}\!\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
Powab{a}^{b} Power
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("7b2c26"),
    Formula(Equal(ChebyshevT(n, x), Sub(Mul(x, ChebyshevT(Sub(n, 1), x)), Mul(Sub(1, Pow(x, 2)), ChebyshevU(Sub(n, 2), x))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC