Fungrim entry: 54c80d

\pi = 4 \sqrt{2} \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n}}{4 n + 1} - 2 \log\!\left(1 + \sqrt{2}\right)

TeX:

\pi = 4 \sqrt{2} \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n}}{4 n + 1} - 2 \log\!\left(1 + \sqrt{2}\right)

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
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`Log`	$\log(z)$	Natural logarithm

Source code for this entry:

Entry(ID("54c80d"),
    Formula(Equal(Pi, Sub(Mul(Mul(4, Sqrt(2)), Sum(Div(Pow(-1, n), Add(Mul(4, n), 1)), For(n, 0, Infinity))), Mul(2, Log(Add(1, Sqrt(2))))))))

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