Fungrim entry: 69d0a3

\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
`AGM`	$\operatorname{agm}\!\left(a, b\right)$	Arithmetic-geometric mean
`ConstI`	$i$	Imaginary unit
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`Gamma`	$\Gamma(z)$	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)))))

Topics using this entry

2021-03-15 19:12:00.328586 UTC