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Fungrim entry: b2d723

Pn ⁣(z‾)=Pn ⁣(z)‾P_{n}\!\left(\overline{z}\right) = \overline{P_{n}\!\left(z\right)}
Assumptions:n∈Z≥0  and⁡  z∈Cn \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
P_{n}\!\left(\overline{z}\right) = \overline{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
Conjugatez‾\overline{z} Complex conjugate
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("b2d723"),
    Formula(Equal(LegendrePolynomial(n, Conjugate(z)), Conjugate(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.

2021-03-15 19:12:00.328586 UTC