# Fungrim entry: 38fa65

$R_F\!\left(x + \lambda, y + \lambda, \lambda\right) + R_F\!\left(x + \mu, y + \mu, \mu\right) = R_F\!\left(x, y, 0\right)\; \text{ where } \mu = \frac{x y}{\lambda}$
Assumptions:$x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; \lambda \in \mathbb{C} \setminus \left(-\infty, 0\right]$
TeX:
R_F\!\left(x + \lambda, y + \lambda, \lambda\right) + R_F\!\left(x + \mu, y + \mu, \mu\right) = R_F\!\left(x, y, 0\right)\; \text{ where } \mu = \frac{x y}{\lambda}

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; \lambda \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
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Source code for this entry:
Entry(ID("38fa65"),
Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)), Element(lamda, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))