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Fungrim entry: 0ed5e2

RF ⁣(0,x,2x)=1x(Γ ⁣(14))242πR_F\!\left(0, x, 2 x\right) = \frac{1}{\sqrt{x}} \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \sqrt{2 \pi}}
Assumptions:x∈Cx \in \mathbb{C}
TeX:
R_F\!\left(0, x, 2 x\right) = \frac{1}{\sqrt{x}} \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \sqrt{2 \pi}}

x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first 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:
Entry(ID("0ed5e2"),
    Formula(Equal(CarlsonRF(0, x, Mul(2, x)), Mul(Div(1, Sqrt(x)), Div(Pow(Gamma(Div(1, 4)), 2), Mul(4, Sqrt(Mul(2, Pi))))))),
    Variables(x),
    Assumptions(Element(x, CC)))

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2021-03-15 19:12:00.328586 UTC