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Fungrim entry: 55d23d

E(m)−(1−m)K(m)=m(1−m)3RD ⁣(0,1,1−m)E(m) - \left(1 - m\right) K(m) = \frac{m \left(1 - m\right)}{3} R_D\!\left(0, 1, 1 - m\right)
Assumptions:m∈Cm \in \mathbb{C}
TeX:
E(m) - \left(1 - m\right) K(m) = \frac{m \left(1 - m\right)}{3} R_D\!\left(0, 1, 1 - m\right)

m \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
EllipticEE(m)E(m) Legendre complete elliptic integral of the second kind
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("55d23d"),
    Formula(Equal(Sub(EllipticE(m), Mul(Sub(1, m), EllipticK(m))), Mul(Div(Mul(m, Sub(1, m)), 3), CarlsonRD(0, 1, Sub(1, m))))),
    Variables(m),
    Assumptions(Element(m, CC)))

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2021-03-15 19:12:00.328586 UTC