Fungrim entry: 0bd544

G = \frac{\pi}{8} \log\!\left(2 + \sqrt{3}\right) + \frac{3}{8} \sum_{n=0}^{\infty} \frac{1}{{\left(2 n + 1\right)}^{2} \cdot {2 n \choose n}}

TeX:

G = \frac{\pi}{8} \log\!\left(2 + \sqrt{3}\right) + \frac{3}{8} \sum_{n=0}^{\infty} \frac{1}{{\left(2 n + 1\right)}^{2} \cdot  {2 n \choose n}}

Definitions:

Fungrim symbol	Notation	Short description
`ConstCatalan`	$G$	Catalan's constant
`Pi`	$\pi$	The constant pi (3.14...)
`Log`	$\log(z)$	Natural logarithm
`Sqrt`	$\sqrt{z}$	Principal square root
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power
`Binomial`	${n \choose k}$	Binomial coefficient
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("0bd544"),
    Formula(Equal(ConstCatalan, Add(Mul(Div(Pi, 8), Log(Add(2, Sqrt(3)))), Mul(Div(3, 8), Sum(Div(1, Mul(Pow(Add(Mul(2, n), 1), 2), Binomial(Mul(2, n), n))), For(n, 0, Infinity)))))))

Topics using this entry

Catalan's constant

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