Fungrim entry: a2e9dd

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

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)

TeX:

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

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)

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
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("a2e9dd"),
    Formula(Equal(CarlsonRG(0, x, Mul(c, x)), Div(Mul(Sqrt(x), EllipticE(Sub(1, c))), 2))),
    Variables(x, c),
    Assumptions(And(Element(x, CC), Element(c, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals