Fungrim entry: 5d0c95

R_G\!\left(x, y, y\right) = \frac{1}{2} \begin{cases} y R_C\!\left(x, y\right) + \sqrt{x}, & y \ne 0\\\sqrt{x}, & y = 0\\ \end{cases}

Assumptions:

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

TeX:

R_G\!\left(x, y, y\right) = \frac{1}{2} \begin{cases} y R_C\!\left(x, y\right) + \sqrt{x}, & y \ne 0\\\sqrt{x}, & y = 0\\ \end{cases}

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

Definitions:

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

Source code for this entry:

Entry(ID("5d0c95"),
    Formula(Equal(CarlsonRG(x, y, y), Mul(Div(1, 2), Cases(Tuple(Add(Mul(y, CarlsonRC(x, y)), Sqrt(x)), NotEqual(y, 0)), Tuple(Sqrt(x), Equal(y, 0)))))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals