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Fungrim entry: 6fce07

2π=∏n=1∞an2   where a1=2,  an=2+an−1\frac{2}{\pi} = \prod_{n=1}^{\infty} \frac{a_{n}}{2}\; \text{ where } a_{1} = \sqrt{2},\;a_{n} = \sqrt{2 + a_{n - 1}}
TeX:
\frac{2}{\pi} = \prod_{n=1}^{\infty} \frac{a_{n}}{2}\; \text{ where } a_{1} = \sqrt{2},\;a_{n} = \sqrt{2 + a_{n - 1}}
Definitions:
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
Product∏nf(n)\prod_{n} f(n) Product
Infinity∞\infty Positive infinity
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("6fce07"),
    Formula(Equal(Div(2, Pi), Where(Product(Div(a_(n), 2), For(n, 1, Infinity)), Def(a_(1), Sqrt(2)), Def(a_(n), Sqrt(Add(2, a_(Sub(n, 1)))))))))

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2021-03-15 19:12:00.328586 UTC