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Fungrim entry: 4b83c6

T2n ⁣(x)=2Tn2 ⁣(x)1T_{2 n}\!\left(x\right) = 2 T_{n}^{2}\!\left(x\right) - 1
Assumptions:nZandxCn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
T_{2 n}\!\left(x\right) = 2 T_{n}^{2}\!\left(x\right) - 1

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("4b83c6"),
    Formula(Equal(ChebyshevT(Mul(2, n), x), Sub(Mul(2, Pow(ChebyshevT(n, x), 2)), 1))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-19 20:12:49.583742 UTC