Fungrim entry: 0745ee

$\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} P_{n}\!\left(z\right) = \left\{x_{n,1}, x_{n,2}, \ldots, x_{n,n}\right\}$
Assumptions:$n \in \mathbb{Z}_{\ge 0}$
TeX:
\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} P_{n}\!\left(z\right) = \left\{x_{n,1}, x_{n,2}, \ldots, x_{n,n}\right\}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Zeros$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$ Zeros (roots) of function
LegendrePolynomial$P_{n}\!\left(z\right)$ Legendre polynomial
CC$\mathbb{C}$ Complex numbers
LegendrePolynomialZero$x_{n,k}$ Legendre polynomial zero
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("0745ee"),
Formula(Equal(Zeros(LegendrePolynomial(n, z), ForElement(z, CC)), Set(LegendrePolynomialZero(n, k), For(k, 1, n)))),
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.

2021-03-15 19:12:00.328586 UTC