Fungrim home page

Fungrim entry: 415911

∣zeros⁡ z∈CPn ⁣(z)∣=n\left|\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} P_{n}\!\left(z\right)\right| = n
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
\left|\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} P_{n}\!\left(z\right)\right| = n

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Cardinality∣S∣\left|S\right| Set cardinality
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("415911"),
    Formula(Equal(Cardinality(Zeros(LegendrePolynomial(n, z), z, Element(z, CC))), 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.

2019-06-18 07:49:59.356594 UTC