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Fungrim entry: 0bd544

G=π8log ⁣(2+3)+38n=01(2n+1)2(2nn)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
ConstCatalanGG Catalan's constant
Piπ\pi The constant pi (3.14...)
Loglog(z)\log(z) Natural logarithm
Sqrtz\sqrt{z} Principal square root
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Binomial(nk){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)))))))

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2020-08-27 09:56:25.682319 UTC