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Fungrim entry: 40fa59

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

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("40fa59"),
    Formula(Equal(HolomorphicDomain(LegendrePolynomial(n, z), z, Union(CC, Set(UnsignedInfinity))), CC)),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

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2019-06-18 07:49:59.356594 UTC