Fungrim entry: c05ed8

R_J\!\left(0, 1, 2, 2\right) = \frac{3 \sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{16 \sqrt{\pi}} - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}

TeX:

R_J\!\left(0, 1, 2, 2\right) = \frac{3 \sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{16 \sqrt{\pi}} - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRJ`	$R_J\!\left(x, y, z, w\right)$	Carlson symmetric elliptic integral of the third kind
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Gamma`	$\Gamma(z)$	Gamma function
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("c05ed8"),
    Formula(Equal(CarlsonRJ(0, 1, 2, 2), Sub(Div(Mul(Mul(3, Sqrt(2)), Pow(Gamma(Div(1, 4)), 2)), Mul(16, Sqrt(Pi))), Div(Mul(Mul(3, Sqrt(2)), Pow(Pi, Div(3, 2))), Mul(2, Pow(Gamma(Div(1, 4)), 2)))))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals