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Fungrim entry: 5a8f57

RJ ⁣(0,y,z,w)=3π4R3/2 ⁣([12,12,1],[y,z,w])R_J\!\left(0, y, z, w\right) = \frac{3 \pi}{4} R_{-3 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, 1\right], \left[y, z, w\right]\right)
Assumptions:yC(,0]  and  zC(,0]  and  wC(,0]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]
TeX:
R_J\!\left(0, y, z, w\right) = \frac{3 \pi}{4} R_{-3 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, 1\right], \left[y, z, w\right]\right)

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]
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
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:
Entry(ID("5a8f57"),
    Formula(Equal(CarlsonRJ(0, y, z, w), Mul(Div(Mul(3, Pi), 4), CarlsonHypergeometricR(Neg(Div(3, 2)), List(Div(1, 2), Div(1, 2), 1), List(y, z, w))))),
    Variables(y, z, w),
    Assumptions(And(Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(w, 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