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Fungrim entry: 42eb01

Tn2 ⁣(x)+(x2−1)Un−12 ⁣(x)=1T_{n}^{2}\!\left(x\right) + \left({x}^{2} - 1\right) U_{n - 1}^{2}\!\left(x\right) = 1
Assumptions:n∈Z  and⁡  x∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{n}^{2}\!\left(x\right) + \left({x}^{2} - 1\right) U_{n - 1}^{2}\!\left(x\right) = 1

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
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("42eb01"),
    Formula(Equal(Add(Pow(ChebyshevT(n, x), 2), Mul(Sub(Pow(x, 2), 1), Pow(ChebyshevU(Sub(n, 1), 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