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Fungrim entry: 8d7b3d

limN1N2n=1Nφ ⁣(n)=3π2\lim_{N \to \infty} \frac{1}{{N}^{2}} \sum_{n=1}^{N} \varphi\!\left(n\right) = \frac{3}{{\pi}^{2}}
TeX:
\lim_{N \to \infty} \frac{1}{{N}^{2}} \sum_{n=1}^{N} \varphi\!\left(n\right) = \frac{3}{{\pi}^{2}}
Definitions:
Fungrim symbol Notation Short description
SequenceLimitlimnaf ⁣(n)\lim_{n \to a} f\!\left(n\right) Limiting value of sequence
Powab{a}^{b} Power
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Infinity\infty Positive infinity
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("8d7b3d"),
    Formula(Equal(SequenceLimit(Mul(Div(1, Pow(N, 2)), Sum(Totient(n), Tuple(n, 1, N))), Var(N), Infinity), Div(3, Pow(ConstPi, 2)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-20 18:07:53.062439 UTC