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Fungrim entry: 42eb01

(Tn ⁣(x))2+(x2−1)(Un−1 ⁣(x))2=1{\left(T_{n}\!\left(x\right)\right)}^{2} + \left({x}^{2} - 1\right) {\left(U_{n - 1}\!\left(x\right)\right)}^{2} = 1
Assumptions:n∈Z and⁡ x∈Cn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
{\left(T_{n}\!\left(x\right)\right)}^{2} + \left({x}^{2} - 1\right) {\left(U_{n - 1}\!\left(x\right)\right)}^{2} = 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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2019-06-18 07:49:59.356594 UTC