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Fungrim entry: 5f09f4

U2n ⁣(x)=Tn ⁣(2x2−1)+Un−1 ⁣(2x2−1)U_{2 n}\!\left(x\right) = T_{n}\!\left(2 {x}^{2} - 1\right) + U_{n - 1}\!\left(2 {x}^{2} - 1\right)
Assumptions:n∈Z  and⁡  x∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
U_{2 n}\!\left(x\right) = T_{n}\!\left(2 {x}^{2} - 1\right) + U_{n - 1}\!\left(2 {x}^{2} - 1\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
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("5f09f4"),
    Formula(Equal(ChebyshevU(Mul(2, n), x), Add(ChebyshevT(n, Sub(Mul(2, Pow(x, 2)), 1)), ChebyshevU(Sub(n, 1), Sub(Mul(2, Pow(x, 2)), 1))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC