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Fungrim entry: 94f646

K(m)−E(m)=m3RD ⁣(0,1−m,1)K(m) - E(m) = \frac{m}{3} R_D\!\left(0, 1 - m, 1\right)
Assumptions:m∈Cm \in \mathbb{C}
TeX:
K(m) - E(m) = \frac{m}{3} R_D\!\left(0, 1 - m, 1\right)

m \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
EllipticEE(m)E(m) Legendre complete elliptic integral of the second 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("94f646"),
    Formula(Equal(Sub(EllipticK(m), EllipticE(m)), Mul(Div(m, 3), CarlsonRD(0, Sub(1, m), 1)))),
    Variables(m),
    Assumptions(Element(m, CC)))

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2021-03-15 19:12:00.328586 UTC