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"),
    Formula(Where(Equal(Add(CarlsonRF(Add(x, lamda), Add(y, lamda), lamda), CarlsonRF(Add(x, mu), Add(y, mu), mu)), CarlsonRF(x, y, 0)), Def(mu, Div(Mul(x, y), lamda)))),
    Variables(x, y, lamda),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)), Element(lamda, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))

Topics using this entry

Carlson symmetric elliptic integrals