Assumptions:
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 | Zeros (roots) of function | |
LegendrePolynomial | Legendre polynomial | |
CC | Complex numbers | |
LegendrePolynomialZero | Legendre polynomial zero | |
ZZGreaterEqual | 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))))