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Fungrim entry: 3f1547

RG ⁣(0,x,2x)=x((Γ ⁣(14))282π+π3/22(Γ ⁣(14))2)R_G\!\left(0, x, 2 x\right) = \sqrt{x} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} + \frac{{\pi}^{3 / 2}}{\sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)
Assumptions:xCx \in \mathbb{C}
R_G\!\left(0, x, 2 x\right) = \sqrt{x} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} + \frac{{\pi}^{3 / 2}}{\sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)

x \in \mathbb{C}
Fungrim symbol Notation Short description
CarlsonRGRG ⁣(x,y,z)R_G\!\left(x, y, z\right) Carlson symmetric elliptic integral of the second kind
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
GammaΓ(z)\Gamma(z) Gamma function
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(CarlsonRG(0, x, Mul(2, x)), Mul(Sqrt(x), Mul(Add(Div(Pow(Gamma(Div(1, 4)), 2), Mul(8, Sqrt(Mul(2, Pi)))), Div(Pow(Pi, Div(3, 2)), Mul(Sqrt(2), Pow(Gamma(Div(1, 4)), 2)))))))),
    Assumptions(Element(x, CC)))

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2021-03-15 19:12:00.328586 UTC