# 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

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