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Fungrim entry: fda800

Tn ⁣(x)=cos⁡ ⁣(nacos⁡(x))T_{n}\!\left(x\right) = \cos\!\left(n \operatorname{acos}(x)\right)
Assumptions:n∈Z  and⁡  x∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{n}\!\left(x\right) = \cos\!\left(n \operatorname{acos}(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
Coscos⁡(z)\cos(z) Cosine
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("fda800"),
    Formula(Equal(ChebyshevT(n, x), Cos(Mul(n, Acos(x))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC