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Fungrim entry: 0649c9

Tn ⁣(x)=Un ⁣(x)Un2 ⁣(x)2T_{n}\!\left(x\right) = \frac{U_{n}\!\left(x\right) - U_{n - 2}\!\left(x\right)}{2}
Assumptions:nZ  and  xCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
T_{n}\!\left(x\right) = \frac{U_{n}\!\left(x\right) - U_{n - 2}\!\left(x\right)}{2}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Fungrim symbol Notation Short description
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
ChebyshevUUn ⁣(x)U_{n}\!\left(x\right) Chebyshev polynomial of the second kind
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(ChebyshevT(n, x), Div(Sub(ChebyshevU(n, x), ChebyshevU(Sub(n, 2), x)), 2))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC