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Fungrim entry: 47dead

K(m)=0111x21mx2dxK(m) = \int_{0}^{1} \frac{1}{\sqrt{1 - {x}^{2}} \sqrt{1 - m {x}^{2}}} \, dx
Assumptions:mC[1,)m \in \mathbb{C} \setminus \left[1, \infty\right)
TeX:
K(m) = \int_{0}^{1} \frac{1}{\sqrt{1 - {x}^{2}} \sqrt{1 - m {x}^{2}}} \, dx

m \in \mathbb{C} \setminus \left[1, \infty\right)
Definitions:
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
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("47dead"),
    Formula(Equal(EllipticK(m), Integral(Div(1, Mul(Sqrt(Sub(1, Pow(x, 2))), Sqrt(Sub(1, Mul(m, Pow(x, 2)))))), For(x, 0, 1)))),
    Variables(m),
    Assumptions(Element(m, SetMinus(CC, ClosedOpenInterval(1, Infinity)))))

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2021-03-15 19:12:00.328586 UTC