Fungrim entry: d0c9ff

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

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
CarlsonRF$R_F\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the first 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("d0c9ff"),
Formula(Equal(CarlsonRF(0, y, z), Mul(Div(Pi, 2), CarlsonHypergeometricR(Neg(Div(1, 2)), List(Div(1, 2), Div(1, 2)), List(y, z))))),
Variables(y, z),
Assumptions(And(Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(z, 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