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Fungrim entry: 415911

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

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Cardinality#S\# S Set cardinality
ZeroszerosxSf(x)\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x) Zeros (roots) of function
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\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), ForElement(z, CC))), n)),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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

2019-12-30 15:00:46.909060 UTC