Fungrim entry: fda084

R_G\!\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)

Assumptions:

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)

TeX:

R_G\!\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)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRG`	$R_G\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the second kind
`CarlsonHypergeometricR`	$R_{-a}\!\left(b, z\right)$	Carlson multivariate hypergeometric function
`CC`	$\mathbb{C}$	Complex numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("fda084"),
    Formula(Equal(CarlsonRG(x, y, z), CarlsonHypergeometricR(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))))))

Fungrim entry: fda084

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