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Fungrim entry: b95ffa

K ⁣(437)=3+23(Γ ⁣(13))3210/3πK\!\left(4 \sqrt{3} - 7\right) = \frac{\sqrt{3 + 2 \sqrt{3}} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3}}{{2}^{10 / 3} \pi}
TeX:
K\!\left(4 \sqrt{3} - 7\right) = \frac{\sqrt{3 + 2 \sqrt{3}} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3}}{{2}^{10 / 3} \pi}
Definitions:
Fungrim symbol Notation Short description
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
GammaΓ(z)\Gamma(z) Gamma function
Piπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("b95ffa"),
    Formula(Equal(EllipticK(Sub(Mul(4, Sqrt(3)), 7)), Div(Mul(Sqrt(Add(3, Mul(2, Sqrt(3)))), Pow(Gamma(Div(1, 3)), 3)), Mul(Pow(2, Div(10, 3)), Pi)))))

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2021-03-15 19:12:00.328586 UTC