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Fungrim entry: 545e8b

RD ⁣(1,1,−1)=−32π8+(32log⁡ ⁣(1+2)4−32)iR_D\!\left(1, 1, -1\right) = -\frac{3 \sqrt{2} \pi}{8} + \left(\frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{4} - \frac{3}{2}\right) i
TeX:
R_D\!\left(1, 1, -1\right) = -\frac{3 \sqrt{2} \pi}{8} + \left(\frac{3 \sqrt{2} \log\!\left(1 + \sqrt{2}\right)}{4} - \frac{3}{2}\right) i
Definitions:
Fungrim symbol Notation Short description
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Loglog⁡(z)\log(z) Natural logarithm
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("545e8b"),
    Formula(Equal(CarlsonRD(1, 1, -1), Add(Neg(Div(Mul(Mul(3, Sqrt(2)), Pi), 8)), Mul(Sub(Div(Mul(Mul(3, Sqrt(2)), Log(Add(1, Sqrt(2)))), 4), Div(3, 2)), ConstI)))))

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2021-03-15 19:12:00.328586 UTC