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Fungrim entry: 0010f3

Pn ⁣(z)=(1)nPn ⁣(z)P_{n}\!\left(-z\right) = {\left(-1\right)}^{n} P_{n}\!\left(z\right)
Assumptions:nZ0andzCn \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
TeX:
P_{n}\!\left(-z\right) = {\left(-1\right)}^{n} P_{n}\!\left(z\right)

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
Powab{a}^{b} Power
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("0010f3"),
    Formula(Equal(LegendrePolynomial(n, Neg(z)), Mul(Pow(-1, n), LegendrePolynomial(n, z)))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(z, CC))))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC