Fungrim entry: 771801

R_D\!\left(x, x, y\right) = \begin{cases} \frac{3}{y - x} \left(R_C\!\left(y, x\right) - \frac{1}{\sqrt{y}}\right), & x \ne y\\{x}^{-3 / 2}, & x = y\\ \end{cases}

Assumptions:

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

TeX:

R_D\!\left(x, x, y\right) = \begin{cases} \frac{3}{y - x} \left(R_C\!\left(y, x\right) - \frac{1}{\sqrt{y}}\right), & x \ne y\\{x}^{-3 / 2}, & x = y\\ \end{cases}

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

Definitions:

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

Source code for this entry:

Entry(ID("771801"),
    Formula(Equal(CarlsonRD(x, x, y), Cases(Tuple(Mul(Div(3, Sub(y, x)), Sub(CarlsonRC(y, x), Div(1, Sqrt(y)))), NotEqual(x, y)), Tuple(Pow(x, Neg(Div(3, 2))), Equal(x, y))))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC))))

Fungrim entry: 771801

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