File:PlotDelta.gif
Summary
| Description |
English: This plot illustrates normalized fluctuations of the prime-counting function on the logarithmic scale.
The red line represents Δ-function, while the blue curve represents similar function where is replaced by , so one can compare the fluctuations with the difference between and . The image was built by Droog_Andrey using Wolfram Mathematica 7.0 as follows: LogLinearPlot[{(PrimePi[x] - RiemannR[x] + 1/Log[x] - ArcTan[Pi/Log[x]]/Pi)*Log[x]/Sqrt[x], (LogIntegral[x] - RiemannR[x] + 1/Log[x] - ArcTan[Pi/Log[x]]/Pi)*Log[x]/Sqrt[x]}, {x, 1, Exp[14]}, PlotPoints -> 10000, PlotRange -> All, PlotStyle -> {Red, Blue}, AxesOrigin -> {1, 0}, AspectRatio -> 1/2, AxesStyle -> Thick, TicksStyle -> Directive[Thick, Bold, 16]] |
| Date | 4 May 2007 (original upload date) |
| Source | Transferred from en.wikipedia to Commons. |
| Author | Droog Andrey at English Wikipedia |
Licensing
 |
This work has been released into the public domain by its author, Droog Andrey at English Wikipedia. This applies worldwide. In some countries this may not be legally possible; if so: Droog Andrey grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
Original upload log
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 2011-01-01 15:39 | 800×400× (39780 bytes) | Droog Andrey | |
| 2011-01-01 15:30 | 1440×720× (91313 bytes) | Droog Andrey | |
| 2008-08-29 17:03 | 800×480× (47370 bytes) | Droog Andrey | ==Summary== This plot illustrates normalized fluctuations of the [[prime-counting function]] <math>\pi(x)</math> on the logarithmic scale. The red curve represents [[Prime-counting function#Formulas_for_prime-counting_functions|delta function]], while th |
| 2007-05-04 06:59 | 800×480× (18505 bytes) | Droog Andrey | This plot illustrates normalized fluctuations of the [[prime counting function]] <math>\pi(x)</math> on the logarithmic scale. The red curve represents [http://en.wikipedia.org/wiki/Prime_counting_function#Formulas_for_prime_counting_functions Delta func |