# 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

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