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Fungrim entry: 6a24ab

Tn ⁣(−x)=(−1)nTn ⁣(x)T_{n}\!\left(-x\right) = {\left(-1\right)}^{n} T_{n}\!\left(x\right)
Assumptions:n∈Z  and⁡  x∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{n}\!\left(-x\right) = {\left(-1\right)}^{n} T_{n}\!\left(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
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("6a24ab"),
    Formula(Equal(ChebyshevT(n, Neg(x)), Mul(Pow(-1, n), ChebyshevT(n, x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC