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Fungrim entry: 62b0c4

RJ ⁣(0,1,1,1)=3(Γ ⁣(14))282π(1i)32π3/22(Γ ⁣(14))2(1+i)R_J\!\left(0, -1, 1, 1\right) = \frac{3 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} \left(1 - i\right) - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}} \left(1 + i\right)
TeX:
R_J\!\left(0, -1, 1, 1\right) = \frac{3 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} \left(1 - i\right) - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}} \left(1 + i\right)
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
Powab{a}^{b} Power
GammaΓ(z)\Gamma(z) Gamma function
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("62b0c4"),
    Formula(Equal(CarlsonRJ(0, -1, 1, 1), Sub(Mul(Div(Mul(3, Pow(Gamma(Div(1, 4)), 2)), Mul(8, Sqrt(Mul(2, Pi)))), Sub(1, ConstI)), Mul(Div(Mul(Mul(3, Sqrt(2)), Pow(Pi, Div(3, 2))), Mul(2, Pow(Gamma(Div(1, 4)), 2))), Add(1, ConstI))))))

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2021-03-15 19:12:00.328586 UTC