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Fungrim entry: 382679

Tn ⁣(x)=2F1 ⁣(n,n,12,1x2)T_{n}\!\left(x\right) = \,{}_2F_1\!\left(-n, n, \frac{1}{2}, \frac{1 - x}{2}\right)
Assumptions:nZ  and  xCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
T_{n}\!\left(x\right) = \,{}_2F_1\!\left(-n, n, \frac{1}{2}, \frac{1 - x}{2}\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
Hypergeometric2F12F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("382679"),
    Formula(Equal(ChebyshevT(n, x), Hypergeometric2F1(Neg(n), n, Div(1, 2), Div(Sub(1, x), 2)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2020-08-27 09:56:25.682319 UTC