Fungrim entry: dabb47

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

TeX:

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

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`Pow`	${a}^{b}$	Power
`Gamma`	$\Gamma(z)$	Gamma function
`AGM`	$\operatorname{agm}\!\left(a, b\right)$	Arithmetic-geometric mean
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("dabb47"),
    Formula(Equal(Pi, Mul(Mul(Div(1, 2), Pow(Gamma(Div(1, 4)), Div(4, 3))), Pow(AGM(1, Sqrt(2)), Div(2, 3))))))

Topics using this entry

2021-03-15 19:12:00.328586 UTC