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Fungrim entry: 69d0a3

agm ⁣(1,i)=2(1+i)π3/2(Γ ⁣(14))2\operatorname{agm}\!\left(1, i\right) = \frac{\sqrt{2} \left(1 + i\right) {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}
TeX:
\operatorname{agm}\!\left(1, i\right) = \frac{\sqrt{2} \left(1 + i\right) {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}
Definitions:
Fungrim symbol Notation Short description
AGMagm ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Piπ\pi The constant pi (3.14...)
GammaΓ(z)\Gamma(z) Gamma function
Source code for this entry:
Entry(ID("69d0a3"),
    Formula(Equal(AGM(1, ConstI), Div(Mul(Mul(Sqrt(2), Add(1, ConstI)), Pow(Pi, Div(3, 2))), Pow(Gamma(Div(1, 4)), 2)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC