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Fungrim entry: 367ac2

(n+1)Pn+1 ⁣(z)(2n+1)zPn ⁣(z)+nPn1 ⁣(z)=0\left(n + 1\right) P_{n + 1}\!\left(z\right) - \left(2 n + 1\right) z P_{n}\!\left(z\right) + n P_{n - 1}\!\left(z\right) = 0
Assumptions:nZ1andzCn \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
TeX:
\left(n + 1\right) P_{n + 1}\!\left(z\right) - \left(2 n + 1\right) z P_{n}\!\left(z\right) + n P_{n - 1}\!\left(z\right) = 0

n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
LegendrePolynomialPn ⁣(z)P_{n}\!\left(z\right) Legendre polynomial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("367ac2"),
    Formula(Equal(Add(Sub(Mul(Add(n, 1), LegendrePolynomial(Add(n, 1), z)), Mul(Mul(Add(Mul(2, n), 1), z), LegendrePolynomial(n, z))), Mul(n, LegendrePolynomial(Sub(n, 1), z))), 0)),
    Variables(n, z),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(z, CC))))

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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