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Fungrim entry: 630eca

K(2)=(Γ ⁣(14))242π(1i)K(2) = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \sqrt{2 \pi}} \left(1 - i\right)
TeX:
K(2) = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}{4 \sqrt{2 \pi}} \left(1 - i\right)
Definitions:
Fungrim symbol Notation Short description
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Powab{a}^{b} Power
GammaΓ(z)\Gamma(z) Gamma function
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("630eca"),
    Formula(Equal(EllipticK(2), Mul(Div(Pow(Gamma(Div(1, 4)), 2), Mul(4, Sqrt(Mul(2, Pi)))), Sub(1, ConstI)))))

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2021-03-15 19:12:00.328586 UTC