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Fungrim entry: 2573ba

E ⁣(π2,1)=2((Γ ⁣(14))28π+π3/2(Γ ⁣(14))2)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)
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)
Fungrim symbol Notation Short description
IncompleteEllipticEE ⁣(ϕ,m)E\!\left(\phi, m\right) Legendre incomplete elliptic integral of the second kind
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
GammaΓ(z)\Gamma(z) Gamma function
Source code for this entry:
    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)))))))

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2021-03-15 19:12:00.328586 UTC