Fungrim entry: e3896e

\operatorname{agm}\!\left(1, \frac{\sqrt{2}}{2}\right) = \frac{2 {\pi}^{3 / 2}}{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{2}}

TeX:

\operatorname{agm}\!\left(1, \frac{\sqrt{2}}{2}\right) = \frac{2 {\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
`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("e3896e"),
    Formula(Equal(AGM(1, Div(Sqrt(2), 2)), Div(Mul(2, Pow(Pi, Div(3, 2))), Pow(Gamma(Div(1, 4)), 2)))))

Topics using this entry

2021-03-15 19:12:00.328586 UTC