File:ChebyshevPsi.png
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ChebyshevPsi.png (499 × 308 pixels, file size: 7 KB, MIME type: image/png)
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Summary
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This graph image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}}.
It is recommended to name the SVG file “ChebyshevPsi.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
| Description |
English: Plot of Chebyshev's function, along with the approximation . This function can be defined in w: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]}}] |
| Date | |
| Source | Own work |
| Author | Dantheox (talk) (Uploads) |
Licensing
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I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:25, 2 July 2006 | | 499 × 308 (7 KB) | wikimediacommons>Dantheox | 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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