# Fungrim entry: 7ded8f

$R_C\!\left(x, y\right) = R_{-1 / 2}\!\left(\left[\frac{1}{2}, 1\right], \left[x, y\right]\right)$
Assumptions:$x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]$
TeX:
R_C\!\left(x, y\right) = R_{-1 / 2}\!\left(\left[\frac{1}{2}, 1\right], \left[x, y\right]\right)

x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]
Definitions:
Fungrim symbol Notation Short description
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first 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
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Source code for this entry:
Entry(ID("7ded8f"),
Formula(Equal(CarlsonRC(x, y), CarlsonHypergeometricR(Neg(Div(1, 2)), List(Div(1, 2), 1), List(x, y)))),
Variables(x, y),
Assumptions(And(Element(x, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(y, 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