# 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

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