Fungrim entry: 40fa59

P_{n}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C}

Assumptions:

n \in \mathbb{Z}_{\ge 1}

TeX:

P_{n}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C}

n \in \mathbb{Z}_{\ge 1}

Definitions:

Fungrim symbol	Notation	Short description
`IsHolomorphic`	$f(z) \text{ is holomorphic at } z = c$	Holomorphic predicate
`LegendrePolynomial`	$P_{n}\!\left(z\right)$	Legendre polynomial
`CC`	$\mathbb{C}$	Complex numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("40fa59"),
    Formula(IsHolomorphic(LegendrePolynomial(n, z), ForElement(z, CC))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

Legendre polynomials

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