# File:ChebyshevPsi.png

Jump to navigation Jump to search

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

Description Plot of Chebyshev's ${\displaystyle \psi }$ function, along with the approximation ${\displaystyle x-\log 2\pi }$. 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]}}]  Own work 02 July 2006 Dantheox (talk) (Uploads) See below.

## Summary

Plot of Chebyshev's ${\displaystyle \psi }$ function, along with the approximation ${\displaystyle x-\log 2\pi }$. 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]}}]


## File history

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

Date/TimeThumbnailDimensionsUserComment
current17:25, 2 July 2006499 × 308 (7 KB)Dantheox (talk | contribs)Plot of Chebyshev's $\psi$ function, along with the approximation $x-\log 2\pi$. 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
The following pages on the English Wikipedia use this file (pages on other projects are not listed):