Cantitruncated cubic honeycomb: Difference between revisions

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== Divisor summatory function==
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This graph illustrates the [[divisor summatory function]] with the leading asymptotic terms subtracted. That is, it is a graph of
 
:<math>D(x)-x\log x - x(2\gamma-1)</math>
 
where <math>D(x)</math> is the divisor summatory function
 
:<math>D(x)=\sum_{n\le x} d(n)</math>
 
and <math>d(n)</math> is the [[divisor function]]. Here, <math>\gamma=0.577\ldots</math> is the [[Euler-Mascheroni constant]]. The graph extends up to <math>x=10^4</math>. The green lines that do not quite bound the picture are a graph of <math>\pm 2x^{7/22}</math> and  give a general scale for the rate of growth for this function. Curiously, note that the function is not centered on the zero axis, but  seems to be closer to the upper curve.
 
== Licensing ==
Created by Linas Vepstas [[User:Linas]] 12 July 2006
 
{{GFDL|migration=relicense}}
 
{{Copy to Wikimedia Commons|bot=Fbot|priority=true}}

Latest revision as of 00:33, 2 March 2014

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