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Fungrim entry: 8a785a

Tn ⁣(x)=2xTn+1 ⁣(x)Tn+2 ⁣(x)T_{n}\!\left(x\right) = 2 x T_{n + 1}\!\left(x\right) - T_{n + 2}\!\left(x\right)
Assumptions:nZandxCn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
T_{n}\!\left(x\right) = 2 x T_{n + 1}\!\left(x\right) - T_{n + 2}\!\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
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("8a785a"),
    Formula(Equal(ChebyshevT(n, x), Sub(Mul(Mul(2, x), ChebyshevT(Add(n, 1), x)), ChebyshevT(Add(n, 2), x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2019-06-18 07:49:59.356594 UTC