# Fungrim entry: 2573ba

$E\!\left(\frac{\pi}{2}, -1\right) = \sqrt{2} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{\pi}} + \frac{{\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)$
TeX:
E\!\left(\frac{\pi}{2}, -1\right) = \sqrt{2} \left(\frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{8 \sqrt{\pi}} + \frac{{\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}\right)
Definitions:
Fungrim symbol Notation Short description
IncompleteEllipticE$E\!\left(\phi, m\right)$ Legendre incomplete elliptic integral of the second kind
Pi$\pi$ The constant pi (3.14...)
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
Gamma$\Gamma(z)$ Gamma function
Source code for this entry:
Entry(ID("2573ba"),
Formula(Equal(IncompleteEllipticE(Div(Pi, 2), -1), Mul(Sqrt(2), Add(Div(Pow(Gamma(Div(1, 4)), 2), Mul(8, Sqrt(Pi))), Div(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