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# Fungrim entry: 5bd0ec

$T_{n}\!\left(\frac{x + {x}^{-1}}{2}\right) = \frac{{x}^{n} + {x}^{-n}}{2}$
Assumptions:$n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C} \setminus \left\{0\right\}$
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
ChebyshevT$T_{n}\!\left(x\right)$ Chebyshev polynomial of the first kind
Pow${a}^{b}$ Power
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ 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))))))

## Topics using this entry

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

2019-06-18 07:49:59.356594 UTC