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Fungrim entry: 420007

π=lim⁡n→∞12((−1)n+1(2n)!B2n)1/(2n)\pi = \lim_{n \to \infty} \frac{1}{2} {\left({\left(-1\right)}^{n + 1} \frac{\left(2 n\right)!}{B_{2 n}}\right)}^{1 / \left(2 n\right)}
TeX:
\pi = \lim_{n \to \infty} \frac{1}{2} {\left({\left(-1\right)}^{n + 1} \frac{\left(2 n\right)!}{B_{2 n}}\right)}^{1 / \left(2 n\right)}
Definitions:
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
SequenceLimitlim⁡n→af(n)\lim_{n \to a} f(n) Limiting value of sequence
Powab{a}^{b} Power
Factorialn!n ! Factorial
BernoulliBBnB_{n} Bernoulli number
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("420007"),
    Formula(Equal(Pi, SequenceLimit(Mul(Div(1, 2), Pow(Mul(Pow(-1, Add(n, 1)), Div(Factorial(Mul(2, n)), BernoulliB(Mul(2, n)))), Div(1, Parentheses(Mul(2, n))))), For(n, Infinity)))))

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2021-03-15 19:12:00.328586 UTC