# Fungrim entry: 9b0385

$\Pi\!\left(\frac{1}{2}, \frac{1}{2}\right) = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \sqrt{\pi}} + \frac{2 {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}$
TeX:
\Pi\!\left(\frac{1}{2}, \frac{1}{2}\right) = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \sqrt{\pi}} + \frac{2 {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}
Definitions:
Fungrim symbol Notation Short description
EllipticPi$\Pi\!\left(n, m\right)$ Legendre complete 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...)
Source code for this entry:
Entry(ID("9b0385"),
Formula(Equal(EllipticPi(Div(1, 2), Div(1, 2)), Add(Div(Pow(Gamma(Div(1, 4)), 2), Mul(4, Sqrt(Pi))), Div(Mul(2, Pow(Pi, Div(3, 2))), Pow(Gamma(Div(1, 4)), 2))))))

## Topics using this entry

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2021-03-15 19:12:00.328586 UTC