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Fungrim entry: b2cd79

RJ ⁣(x,y,z,w)=R3/2 ⁣([12,12,12,1],[x,y,z,w])R_J\!\left(x, y, z, w\right) = R_{-3 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, 1\right], \left[x, y, z, w\right]\right)
Assumptions:xC(,0)  and  yC(,0)  and  zC(,0)  and  wC(,0]  and  ((x0  and  y0)  or  (x0  and  z0)  or  (y0  and  z0))x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; \left(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)
TeX:
R_J\!\left(x, y, z, w\right) = R_{-3 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, 1\right], \left[x, y, z, w\right]\right)

x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; \left(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRJRJ ⁣(x,y,z,w)R_J\!\left(x, y, z, w\right) Carlson symmetric elliptic integral of the third 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:
Entry(ID("b2cd79"),
    Formula(Equal(CarlsonRJ(x, y, z, w), CarlsonHypergeometricR(Neg(Div(3, 2)), List(Div(1, 2), Div(1, 2), Div(1, 2), 1), List(x, y, z, w)))),
    Variables(x, y, z, w),
    Assumptions(And(Element(x, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(y, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(z, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(w, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Or(And(NotEqual(x, 0), NotEqual(y, 0)), And(NotEqual(x, 0), NotEqual(z, 0)), And(NotEqual(y, 0), NotEqual(z, 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