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| Keywords: PlotDelta.gif This plot illustrates normalized fluctuations of the prime-counting function <math>\pi x </math> on the logarithmic scale The red line represents 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 Droog_Andrey using Wolfram Mathematica 7 0 as follows <code>LogLinearPlot PrimePix - RiemannRx + 1/Logx - ArcTanPi/Logx/Pi Logx/Sqrtx LogIntegralx - RiemannRx + 1/Logx - ArcTanPi/Logx/Pi Logx/Sqrtx x 1 Exp14 PlotPoints -> 10000 PlotRange -> All PlotStyle -> Red Blue AxesOrigin -> 1 0 AspectRatio -> 1/2 AxesStyle -> Thick TicksStyle -> DirectiveThick Bold 16</code> en wikipedia 2007-05-04 Droog Andrey wikipedia en Droog Andrey Original upload log en wikipedia PlotDelta gif wikitable - 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 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 Prime numbers Arithmetic functions | ||||
