Chebyshev function: Difference between revisions

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== Summary ==
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Plot of Chebyshev's <math>\psi</math> function, along with the approximation <math>x-\log 2\pi</math>. This function can be defined in [[Mathematica]] by:
 
ψ[n_] := Sum[If[PrimeQ[p], Floor[Log[n]/Log[p]] Log[p], 0], {p, 2, n}]
SetAttributes[ψ, Listable]
 
The above plot was then generated by:
 
  Plot[{ψ[n], n - Log[2π]}, {n, 0, 50},
    AxesLabel -> {n, "ψ(n)"},
    TextStyle -> {FontFamily -> "Times", FontSize -> 16},
    PlotStyle -> {{Hue[0.6], Thickness[0.006]}, {RGBColor[0, 0, 0]}}]
 
== Licensing ==
{{PD-self|date=October 2006}}
 
{{Copy to Wikimedia Commons|bot=Fbot|priority=true|date=March 2012}}

Revision as of 22:51, 28 February 2014

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