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Fungrim entry: 849751

RJ ⁣(x,y,z,w)=iRJ ⁣(x,y,z,w)R_J\!\left(-x, -y, -z, w\right) = -\overline{i R_J\!\left(x, y, z, -w\right)}
Assumptions:x(0,]  and  y(0,]  and  z(0,]  and  w(0,]x \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; w \in \left(0, \infty\right]
R_J\!\left(-x, -y, -z, w\right) = -\overline{i R_J\!\left(x, y, z, -w\right)}

x \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; w \in \left(0, \infty\right]
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
Conjugatez\overline{z} Complex conjugate
ConstIii Imaginary unit
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(CarlsonRJ(Neg(x), Neg(y), Neg(z), w), Neg(Conjugate(Mul(ConstI, CarlsonRJ(x, y, z, Neg(w))))))),
    Variables(x, y, z, w),
    Assumptions(And(Element(x, OpenClosedInterval(0, Infinity)), Element(y, OpenClosedInterval(0, Infinity)), Element(z, OpenClosedInterval(0, Infinity)), Element(w, OpenClosedInterval(0, Infinity)))))

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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