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Fungrim entry: d0c9ff

RF ⁣(0,y,z)=π2R1/2 ⁣([12,12],[y,z])R_F\!\left(0, y, z\right) = \frac{\pi}{2} R_{-1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}\right], \left[y, z\right]\right)
Assumptions:yC(,0]  and  zC(,0]y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right]
R_F\!\left(0, y, z\right) = \frac{\pi}{2} R_{-1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}\right], \left[y, z\right]\right)

y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right]
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...)
CarlsonHypergeometricRRa ⁣(b,z)R_{-a}\!\left(b, z\right) Carlson multivariate hypergeometric function
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(CarlsonRF(0, y, z), Mul(Div(Pi, 2), CarlsonHypergeometricR(Neg(Div(1, 2)), List(Div(1, 2), Div(1, 2)), List(y, z))))),
    Variables(y, z),
    Assumptions(And(Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC