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Fungrim entry: b2fdfe

RF ⁣(0,x,1)=π2 2F1 ⁣(12,12,1,1−x)R_F\!\left(0, x, 1\right) = \frac{\pi}{2} \,{}_2F_1\!\left(\frac{1}{2}, \frac{1}{2}, 1, 1 - x\right)
Assumptions:x∈Cx \in \mathbb{C}
TeX:
R_F\!\left(0, x, 1\right) = \frac{\pi}{2} \,{}_2F_1\!\left(\frac{1}{2}, \frac{1}{2}, 1, 1 - x\right)

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
Piπ\pi The constant pi (3.14...)
Hypergeometric2F1 2F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("b2fdfe"),
    Formula(Equal(CarlsonRF(0, x, 1), Mul(Div(Pi, 2), Hypergeometric2F1(Div(1, 2), Div(1, 2), 1, Sub(1, x))))),
    Variables(x),
    Assumptions(Element(x, CC)))

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2021-03-15 19:12:00.328586 UTC