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Fungrim entry: d43f30

G=12n=04n(2n+1)2(2nn)G = \frac{1}{2} \sum_{n=0}^{\infty} \frac{{4}^{n}}{{\left(2 n + 1\right)}^{2} \cdot {2 n \choose n}}
TeX:
G = \frac{1}{2} \sum_{n=0}^{\infty} \frac{{4}^{n}}{{\left(2 n + 1\right)}^{2} \cdot  {2 n \choose n}}
Definitions:
Fungrim symbol Notation Short description
ConstCatalanGG Catalan's constant
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("d43f30"),
    Formula(Equal(ConstCatalan, Mul(Div(1, 2), Sum(Div(Pow(4, n), 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