Fungrim entry: 7314c4

R_J\!\left(0, y, z, w\right) = \frac{3 \pi}{4} R_{-3 / 2}\!\left(\left[\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right], \left[y, z, w, w\right]\right)

Assumptions:

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}, \frac{1}{2}, \frac{1}{2}\right], \left[y, z, w, 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
`CarlsonRJ`	$R_J\!\left(x, y, z, w\right)$	Carlson symmetric elliptic integral of the third kind
`Pi`	$\pi$	The constant pi (3.14...)
`CarlsonHypergeometricR`	$R_{-a}\!\left(b, z\right)$	Carlson multivariate hypergeometric function
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("7314c4"),
    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), Div(1, 2), Div(1, 2)), List(y, z, w, 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))))))

Topics using this entry

Series representations of Carlson symmetric elliptic integrals