# Fungrim entry: 060366

$R_D\!\left(0, 1, 2\right) = \frac{3 \sqrt{2} {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{16 \sqrt{\pi}} - \frac{3 \sqrt{2} {\pi}^{3 / 2}}{2 {\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}$
TeX:
R_D\!\left(0, 1, 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
CarlsonRD$R_D\!\left(x, y, z\right)$ Degenerate 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("060366"),
Formula(Equal(CarlsonRD(0, 1, 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)))))))

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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