Fungrim entry: 7a168a

R_F\!\left(\lambda x, \lambda y, \lambda z\right) = {\lambda}^{-1 / 2} R_F\!\left(x, y, z\right)

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \lambda \in \left(0, \infty\right)

TeX:

R_F\!\left(\lambda x, \lambda y, \lambda z\right) = {\lambda}^{-1 / 2} R_F\!\left(x, y, z\right)

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \lambda \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first 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("7a168a"),
    Formula(Equal(CarlsonRF(Mul(lamda, x), Mul(lamda, y), Mul(lamda, z)), Mul(Pow(lamda, Neg(Div(1, 2))), CarlsonRF(x, y, z)))),
    Variables(x, y, z, lamda),
    Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), Element(lamda, OpenInterval(0, Infinity)))))

Fungrim entry: 7a168a

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