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| == Summary ==
| | Hello. Let me introduce the writer. Her name is Emilia Shroyer but it's not the most feminine name out there. Minnesota has always been his [http://www.pornextras.info/blog/187567 at home std testing] but his spouse desires them to transfer. My working day occupation is a librarian. To gather badges is what her family members and her appreciate. |
| 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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Revision as of 08:36, 13 February 2014
Hello. Let me introduce the writer. Her name is Emilia Shroyer but it's not the most feminine name out there. Minnesota has always been his at home std testing but his spouse desires them to transfer. My working day occupation is a librarian. To gather badges is what her family members and her appreciate.