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Fungrim entry: de0968

T2n+1 ⁣(x)=2Tn+1 ⁣(x)Tn ⁣(x)−xT_{2 n + 1}\!\left(x\right) = 2 T_{n + 1}\!\left(x\right) T_{n}\!\left(x\right) - x
Assumptions:n∈Z  and⁡  x∈Cn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{2 n + 1}\!\left(x\right) = 2 T_{n + 1}\!\left(x\right) T_{n}\!\left(x\right) - x

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("de0968"),
    Formula(Equal(ChebyshevT(Add(Mul(2, n), 1), x), Sub(Mul(Mul(2, ChebyshevT(Add(n, 1), x)), ChebyshevT(n, x)), x))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC