Assumptions:
TeX:
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]Definitions:
| Fungrim symbol | Notation | Short description |
|---|---|---|
| CarlsonRJ | Carlson symmetric elliptic integral of the third kind | |
| Conjugate | Complex conjugate | |
| ConstI | Imaginary unit | |
| OpenClosedInterval | Open-closed interval | |
| Infinity | Positive infinity |
Source code for this entry:
Entry(ID("849751"),
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)))))