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Fungrim entry: 2ada0f

(Tn ⁣(x))2−Tn−1 ⁣(x)Tn+1 ⁣(x)>0{\left(T_{n}\!\left(x\right)\right)}^{2} - T_{n - 1}\!\left(x\right) T_{n + 1}\!\left(x\right) > 0
Assumptions:n∈Z≥1  and⁡  x∈(−1,1)n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(-1, 1\right)
TeX:
{\left(T_{n}\!\left(x\right)\right)}^{2} - T_{n - 1}\!\left(x\right) T_{n + 1}\!\left(x\right) > 0

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(-1, 1\right)
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
Entry(ID("2ada0f"),
    Formula(Greater(Sub(Pow(Parentheses(ChebyshevT(n, x)), 2), Mul(ChebyshevT(Sub(n, 1), x), ChebyshevT(Add(n, 1), x))), 0)),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(x, OpenInterval(-1, 1)))))

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

2021-03-15 19:12:00.328586 UTC