Fungrim entry: 7cd257

K(m) = \int_{1}^{\infty} \frac{1}{\sqrt{{x}^{2} - 1} \sqrt{{x}^{2} - m}} \, dx

Assumptions:

m \in \mathbb{C} \setminus \left[1, \infty\right)

TeX:

K(m) = \int_{1}^{\infty} \frac{1}{\sqrt{{x}^{2} - 1} \sqrt{{x}^{2} - m}} \, dx

m \in \mathbb{C} \setminus \left[1, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval

Source code for this entry:

Entry(ID("7cd257"),
    Formula(Equal(EllipticK(m), Integral(Div(1, Mul(Sqrt(Sub(Pow(x, 2), 1)), Sqrt(Sub(Pow(x, 2), m)))), For(x, 1, Infinity)))),
    Variables(m),
    Assumptions(Element(m, SetMinus(CC, ClosedOpenInterval(1, Infinity)))))

Topics using this entry

Legendre elliptic integrals

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