Fungrim entry: 6dda7a

R_D\!\left(x, y, z\right) + R_D\!\left(y, z, x\right) + R_D\!\left(z, x, y\right) = \frac{3}{\sqrt{x} \sqrt{y} \sqrt{z}}

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0

Alternative assumptions:

z \ne 0

TeX:

R_D\!\left(x, y, z\right) + R_D\!\left(y, z, x\right) + R_D\!\left(z, x, y\right) = \frac{3}{\sqrt{x} \sqrt{y} \sqrt{z}}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0

z \ne 0

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRD`	$R_D\!\left(x, y, z\right)$	Degenerate Carlson symmetric elliptic integral of the third kind
`Sqrt`	$\sqrt{z}$	Principal square root
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("6dda7a"),
    Formula(Equal(Add(Add(CarlsonRD(x, y, z), CarlsonRD(y, z, x)), CarlsonRD(z, x, y)), Div(3, Mul(Mul(Sqrt(x), Sqrt(y)), Sqrt(z))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), NotEqual(x, 0), NotEqual(y, 0)), NotEqual(z, 0)))

Topics using this entry

Carlson symmetric elliptic integrals