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Fungrim entry: 4c1db8

RJ ⁣(1,1,1,1)=32log ⁣(1+2)43232πi8R_J\!\left(1, -1, -1, 1\right) = \frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{4} - \frac{3}{2} - \frac{3 \sqrt{2} \pi i}{8}
TeX:
R_J\!\left(1, -1, -1, 1\right) = \frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{4} - \frac{3}{2} - \frac{3 \sqrt{2} \pi i}{8}
Definitions:
Fungrim symbol Notation Short description
CarlsonRJRJ ⁣(x,y,z,w)R_J\!\left(x, y, z, w\right) Carlson symmetric elliptic integral of the third kind
Sqrtz\sqrt{z} Principal square root
Loglog(z)\log(z) Natural logarithm
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("4c1db8"),
    Formula(Equal(CarlsonRJ(1, -1, -1, 1), Sub(Sub(Div(Mul(Mul(3, Sqrt(2)), Log(Add(1, Sqrt(2)))), 4), Div(3, 2)), Div(Mul(Mul(Mul(3, Sqrt(2)), Pi), ConstI), 8)))))

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2021-03-15 19:12:00.328586 UTC