Fungrim entry: f6b4a2

R_J\!\left(0, x, x, w\right) = \frac{3 \pi}{2 \left(x \sqrt{w} + w \sqrt{x}\right)}

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(x \notin \left(-\infty, 0\right) \;\mathbin{\operatorname{or}}\; \operatorname{Im}(w) \ge 0\right)

TeX:

R_J\!\left(0, x, x, w\right) = \frac{3 \pi}{2 \left(x \sqrt{w} + w \sqrt{x}\right)}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(x \notin \left(-\infty, 0\right) \;\mathbin{\operatorname{or}}\; \operatorname{Im}(w) \ge 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRJ`	$R_J\!\left(x, y, z, w\right)$	Carlson symmetric elliptic integral of the third kind
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`CC`	$\mathbb{C}$	Complex numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`Im`	$\operatorname{Im}(z)$	Imaginary part

Source code for this entry:

Entry(ID("f6b4a2"),
    Formula(Equal(CarlsonRJ(0, x, x, w), Div(Mul(3, Pi), Mul(2, Add(Mul(x, Sqrt(w)), Mul(w, Sqrt(x))))))),
    Variables(x, w),
    Assumptions(And(Element(x, CC), Element(w, CC), Or(NotElement(x, OpenInterval(Neg(Infinity), 0)), GreaterEqual(Im(w), 0)))))

Fungrim entry: f6b4a2

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