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Fungrim entry: f88596

limNq=1N#Gq12N2=6π2\lim_{N \to \infty} \frac{\sum_{q=1}^{N} \# G_{q}}{\frac{1}{2} {N}^{2}} = \frac{6}{{\pi}^{2}}
TeX:
\lim_{N \to \infty} \frac{\sum_{q=1}^{N} \# G_{q}}{\frac{1}{2} {N}^{2}} = \frac{6}{{\pi}^{2}}
Definitions:
Fungrim symbol Notation Short description
SequenceLimitlimnaf ⁣(n)\lim_{n \to a} f\!\left(n\right) Limiting value of sequence
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Cardinality#S\# S Set cardinality
DirichletGroupGqG_{q} Dirichlet characters with given modulus
Powab{a}^{b} Power
Infinity\infty Positive infinity
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("f88596"),
    Formula(Equal(SequenceLimit(Div(Sum(Cardinality(DirichletGroup(q)), Tuple(q, 1, N)), Mul(Div(1, 2), Pow(N, 2))), N, Infinity), Div(6, 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.

2019-09-15 13:58:57.282983 UTC