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Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x
#3
The character of convergence of the mean to








can be seen from this graph where first 150 iterations of 100 points x=0.01 step 0.01 = 0.99 are plotted on top of each other.





   

The limited spread (max-min) of each iteration is also visible with such linear choice and size of steps.

I guess this is somehow related to tree functions (which are related to Lambert function) and iterated logarithms. Just to remember always that studying constant is studying Lambert Wo(1)= so generalizations are possible if things are positioned correctly. So far I do not see them, but I see what to read next.

Ivars
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RE: Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x - by Ivars - 03/26/2008, 11:51 AM

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