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Fungrim entry: 42c7f1

RC ⁣(x,y)=R1/2 ⁣([12,12,12],[x,y,y])R_C\!\left(x, y\right) = R_{-1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right], \left[x, y, y\right]\right)
Assumptions:xC(,0)  and  yC(,0]x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]
R_C\!\left(x, y\right) = R_{-1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right], \left[x, y, y\right]\right)

x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
CarlsonHypergeometricRRa ⁣(b,z)R_{-a}\!\left(b, z\right) Carlson multivariate hypergeometric function
CCC\mathbb{C} Complex numbers
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Source code for this entry:
    Formula(Equal(CarlsonRC(x, y), CarlsonHypergeometricR(Neg(Div(1, 2)), List(Div(1, 2), Div(1, 2), Div(1, 2)), List(x, y, y)))),
    Variables(x, y),
    Assumptions(And(Element(x, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(y, 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