Fungrim entry: 3f1547

R_G\!\left(0, x, 2 x\right) = \sqrt{x} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} + \frac{{\pi}^{3 / 2}}{\sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)

Assumptions:

x \in \mathbb{C}

TeX:

R_G\!\left(0, x, 2 x\right) = \sqrt{x} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{2 \pi}} + \frac{{\pi}^{3 / 2}}{\sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)

x \in \mathbb{C}

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
`Pow`	${a}^{b}$	Power
`Gamma`	$\Gamma(z)$	Gamma function
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("3f1547"),
    Formula(Equal(CarlsonRG(0, x, Mul(2, x)), Mul(Sqrt(x), Mul(Add(Div(Pow(Gamma(Div(1, 4)), 2), Mul(8, Sqrt(Mul(2, Pi)))), Div(Pow(Pi, Div(3, 2)), Mul(Sqrt(2), Pow(Gamma(Div(1, 4)), 2)))))))),
    Variables(x),
    Assumptions(Element(x, CC)))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals