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| == Summary ==
| | She is recognized by the name of Myrtle Shryock. Managing people is what I do and the salary has been truly fulfilling. Years ago we moved to North Dakota. To do aerobics is a thing that I'm completely addicted to.<br><br>Also visit my blog: [http://essexsinglesnights.co.uk/groups/cures-for-any-candida-tips-to-use-now/ at home std test] |
| Graph of [[Chebyshev function]], with the leading terms subtracted, for values of ''n'' from 1 to 10,000. Note the remarkably chaotic, unpredictable movement of this function.
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| More precisely, this is a graph of
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| :<math>\psi(x)-x+\log(\pi)</math>
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| The green lines above and below provide a limit of <math>\pm\frac12\sqrt{x}</math>. Note that the function occasionally exceeds this bound; a theorem stated by [[Erhard Schmidt]] in 1903 shows that, for ''any'' real, positive ''K'', there are values of ''x'' such that
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| :<math>\psi(x)-x < -K\sqrt{x}</math>
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| and
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| :<math>\psi(x)-x > K\sqrt{x}</math>
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| infinitely often.
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| ==See also==
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| [[Image:Chebyshev-big.svg|thumb|left|Chebyshev function to 10M]]
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| == Licensing ==
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| Created by [[User:Linas]], Linas Vepstas, 3 July 2006
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| {{GFDL|migration=relicense}}
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| ==Source code==
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| Created with [[gnuplot]], with the following markup:
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| set term svg
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| set out 'chebyshev.svg'
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| set data style lines
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| unset zeroaxis
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| set xtics border
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| set ytics border
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| set bmargin 5
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| set lmargin 7
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| set title "Chebyshev (summatory von Mangoldt) function"
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| set xlabel "n" 1,0
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| set ylabel "psi(n)-n+log(pi)" 1, 0
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| plot "chebyshev.dat" using 1:2 title "" with lines linewidth 2
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| {{Copy to Wikimedia Commons|bot=Fbot|priority=true}}
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Latest revision as of 08:32, 17 October 2014
She is recognized by the name of Myrtle Shryock. Managing people is what I do and the salary has been truly fulfilling. Years ago we moved to North Dakota. To do aerobics is a thing that I'm completely addicted to.
Also visit my blog: at home std test