# Fungrim entry: 4e21c7

$R_J\!\left(\lambda x, \lambda y, \lambda z, \lambda w\right) = {\lambda}^{-3 / 2} R_J\!\left(x, y, z, w\right)$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \lambda \in \left(0, \infty\right)$
TeX:
R_J\!\left(\lambda x, \lambda y, \lambda z, \lambda w\right) = {\lambda}^{-3 / 2} R_J\!\left(x, y, z, w\right)

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \lambda \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRJ$R_J\!\left(x, y, z, w\right)$ Carlson symmetric elliptic integral of the third kind
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("4e21c7"),
Formula(Equal(CarlsonRJ(Mul(lamda, x), Mul(lamda, y), Mul(lamda, z), Mul(lamda, w)), Mul(Pow(lamda, Neg(Div(3, 2))), CarlsonRJ(x, y, z, w)))),
Variables(x, y, z, w, lamda),
Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), Element(w, CC), Element(lamda, OpenInterval(0, Infinity)))))

## 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