(02/16/2015, 12:03 AM)Kouznetsov Wrote:(02/15/2015, 05:23 PM)tommy1729 Wrote: Maybe I should read somewhere again but I wonder how tetration is related to (laser) physics ?Formalism of superfunctions can be used both, for evaluation of tetration and in (laser) physics.
I wanted to use tetration for representation of large numbers;
in particular, for the normalisation factor of approximations of the multi-particle wave function; in particular, for the Bose–Einstein condensate. Lasers are used in the preparation.
That time, I was surprised, that tetration is not yet developed, so, I upset with mathematicians. I think, they were supposed to do this job in the past century. (Say, in 1950; perhaps, the bolsheviks and nazi just killed the most of Russian and German mathematicians, who could do that).
So, I did the computational part by myself for natural tetration. Then Henryk asked me to do the same for various values of base... If you are interested in the history of science, you may trace this process in details by the list of my publications.. Then I had declared, that I can construct a superfunction for any growing holomorphic function. Including the transfer function of a laser amplifier:
D.Kouznetsov. Superfunctions for amplifiers. Optical Review, July 2013, Volume 20, Issue 4, pp 321-326.
http://link.springer.com/article/10.1007...013-0058-6
I am curious: how large are these numbers which occur in this Bose-Einstein condensate physics, which require tetration to write down? And also what the advantage would be of using a smooth and holomorphic tetration function (which is more complicated to evaluate) as opposed to just "iterated-EXP", i.e. notation of the form \( \exp_b^n(x) \) for some whole-number \( n \), base \( b \) and \( x \) in the range \( [1, b) \), analogous to exponential scientific notation, which does not use the smooth-&-holomorphic extension of the exponential?
