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Fungrim entry: 5bd0ec

Tn ⁣(x+x12)=xn+xn2T_{n}\!\left(\frac{x + {x}^{-1}}{2}\right) = \frac{{x}^{n} + {x}^{-n}}{2}
Assumptions:nZandxC{0}n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C} \setminus \left\{0\right\}
TeX:
T_{n}\!\left(\frac{x + {x}^{-1}}{2}\right) = \frac{{x}^{n} + {x}^{-n}}{2}

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C} \setminus \left\{0\right\}
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("5bd0ec"),
    Formula(Equal(ChebyshevT(n, Div(Add(x, Pow(x, -1)), 2)), Div(Add(Pow(x, n), Pow(x, Neg(n))), 2))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, SetMinus(CC, Set(0))))))

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

2019-12-11 23:01:54.699850 UTC