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Fungrim entry: f4b3fa

Tn ⁣(cos⁡ ⁣(x))=cos⁡ ⁣(nx)T_{n}\!\left(\cos\!\left(x\right)\right) = \cos\!\left(n x\right)
Assumptions:n∈Z and⁡ x∈Cn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
T_{n}\!\left(\cos\!\left(x\right)\right) = \cos\!\left(n 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
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f4b3fa"),
    Formula(Equal(ChebyshevT(n, Cos(x)), Cos(Mul(n, x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2019-06-18 07:49:59.356594 UTC