Volterra series: Difference between revisions

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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.
 
More precisely, this is a graph of
 
:<math>\psi(x)-x+\log(\pi)</math>
 
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
 
:<math>\psi(x)-x < -K\sqrt{x}</math>
 
and
:<math>\psi(x)-x > K\sqrt{x}</math>
 
infinitely often.
 
==See also==
[[Image:Chebyshev-big.svg|thumb|left|Chebyshev function to 10M]]
 
== Licensing ==
Created by [[User:Linas]], Linas Vepstas, 3 July 2006
 
{{GFDL|migration=relicense}}
 
==Source code==
Created with [[gnuplot]], with the following markup:
 
set term svg
set out 'chebyshev.svg'
set data style lines
unset zeroaxis
set xtics border
set ytics border
set bmargin 5
set lmargin 7
set title "Chebyshev (summatory von Mangoldt) function"
set xlabel "n" 1,0
set ylabel "psi(n)-n+log(pi)" 1, 0
plot "chebyshev.dat" using 1:2 title "" with lines linewidth 2
{{Copy to Wikimedia Commons|bot=Fbot|priority=true}}

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

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