Fungrim home page

Fungrim entry: b0c84b

(Tn ⁣(x))2Tn1 ⁣(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) \ge 0
Assumptions:nZ1andx[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) \ge 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
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
ClosedInterval[a,b]\left[a, b\right] Closed interval
Source code for this entry:
Entry(ID("b0c84b"),
    Formula(GreaterEqual(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, ClosedInterval(-1, 1)))))

Topics using this entry

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

2019-08-19 14:38:23.809000 UTC