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Fungrim entry: 190843

E(m)=0π/21msin2 ⁣(x)dxE(m) = \int_{0}^{\pi / 2} \sqrt{1 - m \sin^{2}\!\left(x\right)} \, dx
Assumptions:mCm \in \mathbb{C}
TeX:
E(m) = \int_{0}^{\pi / 2} \sqrt{1 - m \sin^{2}\!\left(x\right)} \, dx

m \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
EllipticEE(m)E(m) Legendre complete elliptic integral of the second kind
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("190843"),
    Formula(Equal(EllipticE(m), Integral(Sqrt(Sub(1, Mul(m, Pow(Sin(x), 2)))), For(x, 0, Div(Pi, 2))))),
    Variables(m),
    Assumptions(Element(m, CC)))

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2021-03-15 19:12:00.328586 UTC