Fungrim entry: 62b0c4

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

TeX:

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

Definitions:

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

Source code for this entry:

Entry(ID("62b0c4"),
    Formula(Equal(CarlsonRJ(0, -1, 1, 1), Sub(Mul(Div(Mul(3, Pow(Gamma(Div(1, 4)), 2)), Mul(8, Sqrt(Mul(2, Pi)))), Sub(1, ConstI)), Mul(Div(Mul(Mul(3, Sqrt(2)), Pow(Pi, Div(3, 2))), Mul(2, Pow(Gamma(Div(1, 4)), 2))), Add(1, ConstI))))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals