Fungrim entry: 120284

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

Assumptions:

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

TeX:

R_G\!\left(x, x, y\right) = \frac{1}{2} \begin{cases} x R_C\!\left(y, x\right) + \sqrt{y}, & x \ne 0\\\sqrt{y}, & x = 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("120284"),
    Formula(Equal(CarlsonRG(x, x, y), Mul(Div(1, 2), Cases(Tuple(Add(Mul(x, CarlsonRC(y, x)), Sqrt(y)), NotEqual(x, 0)), Tuple(Sqrt(y), Equal(x, 0)))))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC))))

Fungrim entry: 120284

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