Fungrim home page

Fungrim entry: 54c80d

π=42n=0(1)n4n+12log ⁣(1+2)\pi = 4 \sqrt{2} \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n}}{4 n + 1} - 2 \log\!\left(1 + \sqrt{2}\right)
\pi = 4 \sqrt{2} \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n}}{4 n + 1} - 2 \log\!\left(1 + \sqrt{2}\right)
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Infinity\infty Positive infinity
Loglog(z)\log(z) Natural logarithm
Source code for this entry:
    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