Topological derivative: Difference between revisions

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==Summary==
The writer is called Wilber Pegues. Ohio is where her house is. My working day job is an invoicing officer but I've already utilized for another 1. What me and my family love psychic ([http://cspl.postech.ac.kr/zboard/Membersonly/144571 postech.ac.kr]) is bungee leaping but I've been taking on new things lately.
This plot illustrates normalized fluctuations of the [[prime-counting function]] <math>\pi(x)</math> on the logarithmic scale.
 
The red line represents [[Prime-counting function#Formulas_for_prime-counting_functions|Δ-function]], while the blue curve represents similar function where <math>\pi_0(x)</math> is replaced by <math>\mathrm{li}(x)</math>, so one can compare the fluctuations with the difference between <math>\pi(x)</math> and <math>\mathrm{li}(x)</math>.
 
The image was built by [[User:Droog_Andrey|Droog_Andrey]] using Wolfram Mathematica 7.0 as follows:
 
<code>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]]</code>
 
== Licensing ==
{{PD-self|date=May 2007}}
 
{{Copy to Wikimedia Commons|bot=Fbot|priority=true|date=March 2012}}

Latest revision as of 10:09, 3 September 2014

The writer is called Wilber Pegues. Ohio is where her house is. My working day job is an invoicing officer but I've already utilized for another 1. What me and my family love psychic (postech.ac.kr) is bungee leaping but I've been taking on new things lately.

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