Assumptions:
TeX:
R_F\!\left(x, y, z\right) = R_{-1 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right], \left[x, y, z\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}}\; \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 |
|---|---|---|
| CarlsonRF | Carlson symmetric elliptic integral of the first kind | |
| CarlsonHypergeometricR | Carlson multivariate hypergeometric function | |
| CC | Complex numbers | |
| OpenInterval | Open interval | |
| Infinity | Positive infinity |
Source code for this entry:
Entry(ID("8f71cb"),
Formula(Equal(CarlsonRF(x, y, z), CarlsonHypergeometricR(Neg(Div(1, 2)), List(Div(1, 2), Div(1, 2), Div(1, 2)), List(x, y, z)))),
Variables(x, y, z),
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))), Or(And(NotEqual(x, 0), NotEqual(y, 0)), And(NotEqual(x, 0), NotEqual(z, 0)), And(NotEqual(y, 0), NotEqual(z, 0))))))