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Fungrim entry: 40fa59

Pn ⁣(z) is holomorphic on zCP_{n}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C}
Assumptions:nZ1n \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
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
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("40fa59"),
    Formula(IsHolomorphic(LegendrePolynomial(n, z), ForElement(z, CC))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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

2019-11-19 15:10:20.037976 UTC