Fungrim home page

Fungrim entry: 752619

2E(m)−K(m)=π2 2F1 ⁣(−12,32,1,m)2 E(m) - K(m) = \frac{\pi}{2} \,{}_2F_1\!\left(-\frac{1}{2}, \frac{3}{2}, 1, m\right)
Assumptions:m∈Cm \in \mathbb{C}
TeX:
2 E(m) - K(m) = \frac{\pi}{2} \,{}_2F_1\!\left(-\frac{1}{2}, \frac{3}{2}, 1, m\right)

m \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
EllipticEE(m)E(m) Legendre complete elliptic integral of the second kind
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Piπ\pi The constant pi (3.14...)
Hypergeometric2F1 2F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("752619"),
    Formula(Equal(Sub(Mul(2, EllipticE(m)), EllipticK(m)), Mul(Div(Pi, 2), Hypergeometric2F1(Neg(Div(1, 2)), Div(3, 2), 1, m)))),
    Variables(m),
    Assumptions(Element(m, 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