File:ChebyshevPsi.png

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ChebyshevPsi.png(499 × 308 pixels, file size: 7 KB, MIME type: image/png)

Description

Plot of Chebyshev's function, along with the approximation . 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]}}]
Source

Own work

Date

02 July 2006

Author

Dantheox (talk) (Uploads)

Permission
(Reusing this file)

See below.


Summary[edit]

Plot of Chebyshev's function, along with the approximation . 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[edit]

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current17:25, 2 July 2006Thumbnail for version as of 17:25, 2 July 2006499 × 308 (7 KB)Dantheox (talk | contribs)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, Listabl
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