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Fungrim entry: df439e

zeroszCPn ⁣(z)(1,1)\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} P_{n}\!\left(z\right) \subset \left(-1, 1\right)
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} P_{n}\!\left(z\right) \subset \left(-1, 1\right)

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
ZeroszerosP(x)f ⁣(x)\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right) Zeros (roots) of function
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
CCC\mathbb{C} Complex numbers
OpenInterval(a,b)\left(a, b\right) Open interval
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("df439e"),
    Formula(Subset(Zeros(LegendrePolynomial(n, z), z, Element(z, CC)), OpenInterval(-1, 1))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

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

2019-08-21 11:44:15.926409 UTC