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Fungrim entry: c05ed8

RJ ⁣(0,1,2,2)=32(Γ ⁣(14))216π32π3/22(Γ ⁣(14))2R_J\!\left(0, 1, 2, 2\right) = \frac{3 \sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{16 \sqrt{\pi}} - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}
TeX:
R_J\!\left(0, 1, 2, 2\right) = \frac{3 \sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{16 \sqrt{\pi}} - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}
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
Powab{a}^{b} Power
GammaΓ(z)\Gamma(z) Gamma function
Piπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("c05ed8"),
    Formula(Equal(CarlsonRJ(0, 1, 2, 2), Sub(Div(Mul(Mul(3, Sqrt(2)), Pow(Gamma(Div(1, 4)), 2)), Mul(16, Sqrt(Pi))), Div(Mul(Mul(3, Sqrt(2)), Pow(Pi, Div(3, 2))), Mul(2, Pow(Gamma(Div(1, 4)), 2)))))))

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2021-03-15 19:12:00.328586 UTC