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Fungrim entry: d36fd7

poles⁡ z∈C∪{∞~}Pn ⁣(z)={∞~}\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C} \cup \left\{{\tilde \infty}\right\}} P_{n}\!\left(z\right) = \left\{{\tilde \infty}\right\}
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C} \cup \left\{{\tilde \infty}\right\}} P_{n}\!\left(z\right) = \left\{{\tilde \infty}\right\}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
CCC\mathbb{C} Complex numbers
UnsignedInfinity∞~{\tilde \infty} Unsigned infinity
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("d36fd7"),
    Formula(Equal(Poles(LegendrePolynomial(n, z), ForElement(z, Union(CC, Set(UnsignedInfinity)))), Set(UnsignedInfinity))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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