Fungrim entry: 3b6175

R_J\!\left(0, y, z, \sqrt{y} \sqrt{z}\right) = \frac{3}{2 \sqrt{y} \sqrt{z}} R_F\!\left(0, y, z\right)

Assumptions:

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

TeX:

R_J\!\left(0, y, z, \sqrt{y} \sqrt{z}\right) = \frac{3}{2 \sqrt{y} \sqrt{z}} R_F\!\left(0, y, z\right)

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

Definitions:

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

Source code for this entry:

Entry(ID("3b6175"),
    Formula(Equal(CarlsonRJ(0, y, z, Mul(Sqrt(y), Sqrt(z))), Mul(Div(3, Mul(2, Mul(Sqrt(y), Sqrt(z)))), CarlsonRF(0, y, z)))),
    Variables(y, z),
    Assumptions(And(Element(y, CC), Element(z, CC))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals