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Fungrim entry: 7cd257

K(m)=11x21x2mdxK(m) = \int_{1}^{\infty} \frac{1}{\sqrt{{x}^{2} - 1} \sqrt{{x}^{2} - m}} \, dx
Assumptions:mC[1,)m \in \mathbb{C} \setminus \left[1, \infty\right)
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)
Fungrim symbol Notation Short description
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Source code for this entry:
    Formula(Equal(EllipticK(m), Integral(Div(1, Mul(Sqrt(Sub(Pow(x, 2), 1)), Sqrt(Sub(Pow(x, 2), m)))), For(x, 1, Infinity)))),
    Assumptions(Element(m, SetMinus(CC, ClosedOpenInterval(1, Infinity)))))

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2021-03-15 19:12:00.328586 UTC