Fungrim entry: 674afa

P_{2 n}\!\left(0\right) = \frac{{\left(-1\right)}^{n}}{{4}^{n}} {2 n \choose n}

Assumptions:

n \in \mathbb{Z}_{\ge 0}

TeX:

P_{2 n}\!\left(0\right) = \frac{{\left(-1\right)}^{n}}{{4}^{n}} {2 n \choose n}

n \in \mathbb{Z}_{\ge 0}

Definitions:

Fungrim symbol	Notation	Short description
`LegendrePolynomial`	$P_{n}\!\left(z\right)$	Legendre polynomial
`Pow`	${a}^{b}$	Power
`Binomial`	${n \choose k}$	Binomial coefficient
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("674afa"),
    Formula(Equal(LegendrePolynomial(Mul(2, n), 0), Mul(Div(Pow(-1, n), Pow(4, n)), Binomial(Mul(2, n), n)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

Legendre polynomials

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