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April 28th, 2013, 02:04 AM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Limit involving 1/2height superexponential
Hi, Does the limit converges : I initially guessed that it's somewhat << log(n) but I think it can be tighten up to << n^? for some reasonably small ? > 0. Thanks, Balarka . 
April 28th, 2013, 07:21 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Limit involving 1/2height superexponential
What definition are you using for ? I'm accustomed to seeing only the restriction to the naturals for the superexponent (though I've seen a few attempts to generalize it). Unrelated: this is the single ugliest notation I know of in mathematics. 
April 28th, 2013, 07:49 AM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Limit involving 1/2height superexponential Quote:
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April 29th, 2013, 05:56 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Limit involving 1/2height superexponential Quote:
Quote:
http://www.digizeitschriften.de/dms/img ... N002175851 I don't read German...  
April 29th, 2013, 06:45 AM  #5  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Limit involving 1/2height superexponential Quote:
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Trappman explains Kneser's method excellently and even for a nonprofessional like me can understand it completely.  
April 29th, 2013, 07:03 AM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Limit involving 1/2height superexponential Quote:
EDIT : The calculations above have errors since the sum isn't really an upper bound for the one of interest, instead, it's a lower bound. Which means, proving that diverges would prove that diverges. So, the problem is being reduced to a fairly easy Real analysis question, does converges or diverges? I know it's likely that this will diverge since is not Cesaro summable, but a rigorous proof would be nice to see. Balarka .  

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1 or 2height, involving, limit, superexponential 
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