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Fungrim entry: 7e882c

Tm ⁣(Tn ⁣(x))=Tmn ⁣(x)T_{m}\!\left(T_{n}\!\left(x\right)\right) = T_{m n}\!\left(x\right)
Assumptions:m∈Z  and⁡  n∈Z  and⁡  x∈Cm \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{m}\!\left(T_{n}\!\left(x\right)\right) = T_{m n}\!\left(x\right)

m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; 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("7e882c"),
    Formula(Equal(ChebyshevT(m, ChebyshevT(n, x)), ChebyshevT(Mul(m, n), x))),
    Variables(m, n, x),
    Assumptions(And(Element(m, ZZ), Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC