Fungrim entry: 7cddc6

R_G\!\left(0, x, y\right) = \frac{\sqrt{x} E\!\left(1 - \frac{y}{x}\right)}{2}

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(x) - \arg(y)\right| < \pi

TeX:

R_G\!\left(0, x, y\right) = \frac{\sqrt{x} E\!\left(1 - \frac{y}{x}\right)}{2}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(x) - \arg(y)\right| < \pi

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRG`	$R_G\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the second kind
`Sqrt`	$\sqrt{z}$	Principal square root
`EllipticE`	$E(m)$	Legendre complete elliptic integral of the second kind
`CC`	$\mathbb{C}$	Complex numbers
`Abs`	$\left\|z\right\|$	Absolute value
`Arg`	$\arg(z)$	Complex argument
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("7cddc6"),
    Formula(Equal(CarlsonRG(0, x, y), Div(Mul(Sqrt(x), EllipticE(Sub(1, Div(y, x)))), 2))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC), Less(Abs(Sub(Arg(x), Arg(y))), Pi))))

Fungrim entry: 7cddc6

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