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Fungrim entry: 41cf8e

E(m)=1m3(RD ⁣(0,1m,1)+RD ⁣(0,1,1m))E(m) = \frac{1 - m}{3} \left(R_D\!\left(0, 1 - m, 1\right) + R_D\!\left(0, 1, 1 - m\right)\right)
Assumptions:mC  and  m1m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \ne 1
E(m) = \frac{1 - m}{3} \left(R_D\!\left(0, 1 - m, 1\right) + R_D\!\left(0, 1, 1 - m\right)\right)

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \ne 1
Fungrim symbol Notation Short description
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:
    Formula(Equal(EllipticE(m), Mul(Div(Sub(1, m), 3), Add(CarlsonRD(0, Sub(1, m), 1), CarlsonRD(0, 1, Sub(1, m)))))),
    Assumptions(And(Element(m, CC), NotEqual(m, 1))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC