Fungrim entry: 8519dd

R_F\!\left(0, \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{4}}{32 \pi}, \frac{-{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{4}}{32 \pi}\right) = 1 - i

TeX:

R_F\!\left(0, \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{4}}{32 \pi}, \frac{-{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{4}}{32 \pi}\right) = 1 - i

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`Pow`	${a}^{b}$	Power
`Gamma`	$\Gamma(z)$	Gamma function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit

Source code for this entry:

Entry(ID("8519dd"),
    Formula(Equal(CarlsonRF(0, Div(Pow(Gamma(Div(1, 4)), 4), Mul(32, Pi)), Div(Neg(Pow(Gamma(Div(1, 4)), 4)), Mul(32, Pi))), Sub(1, ConstI))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC