Fungrim entry: 1faf7a

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

Assumptions:

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

TeX:

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

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \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
`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("1faf7a"),
    Formula(Equal(CarlsonRJ(x, x, x, w), Cases(Tuple(Mul(Div(3, Sub(x, w)), Sub(CarlsonRC(x, w), Div(1, Sqrt(x)))), NotEqual(x, w)), Tuple(Pow(w, Neg(Div(3, 2))), Equal(x, w))))),
    Variables(x, w),
    Assumptions(And(Element(x, CC), Element(w, CC))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals