Fungrim entry: 367ac2

\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:

n \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
`LegendrePolynomial`	$P_{n}\!\left(z\right)$	Legendre polynomial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	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))))

Topics using this entry

Legendre polynomials