Fungrim entry: 9395fc

$P_{n}\!\left(z\right) = \,{}_2F_1\!\left(-n, n + 1, 1, \frac{1 - z}{2}\right)$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}$
TeX:
P_{n}\!\left(z\right) = \,{}_2F_1\!\left(-n, n + 1, 1, \frac{1 - z}{2}\right)

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
LegendrePolynomial$P_{n}\!\left(z\right)$ Legendre polynomial
Hypergeometric2F1$\,{}_2F_1\!\left(a, b, c, z\right)$ Gauss hypergeometric function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("9395fc"),
Formula(Equal(LegendrePolynomial(n, z), Hypergeometric2F1(Neg(n), Add(n, 1), 1, Div(Sub(1, z), 2)))),
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.

2019-12-11 23:01:54.699850 UTC