Fungrim entry: 6b9f81

\frac{1}{\pi} = \frac{2 \sqrt{2}}{9801} \sum_{n=0}^{\infty} \frac{\left(4 n\right)! \left(1103 + 26390 n\right)}{{\left(n !\right)}^{4} \cdot {396}^{4 n}}

TeX:

\frac{1}{\pi} = \frac{2 \sqrt{2}}{9801} \sum_{n=0}^{\infty} \frac{\left(4 n\right)! \left(1103 + 26390 n\right)}{{\left(n !\right)}^{4} \cdot  {396}^{4 n}}

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`Sum`	$\sum_{n} f(n)$	Sum
`Factorial`	$n !$	Factorial
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("6b9f81"),
    Formula(Equal(Div(1, Pi), Mul(Div(Mul(2, Sqrt(2)), 9801), Sum(Div(Mul(Factorial(Mul(4, n)), Add(1103, Mul(26390, n))), Mul(Pow(Factorial(n), 4), Pow(396, Mul(4, n)))), For(n, 0, Infinity))))))

Topics using this entry

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