
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 938 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:
Quote:
 
April 29th, 2013, 05:56 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 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:
Quote:
Quote:
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 .  

Tags 
1 or 2height, involving, limit, superexponential 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
limit involving 2 sequences  Urania  Calculus  8  March 6th, 2014 08:10 AM 
The Reciprocal Superexponential Sum  mathbalarka  Calculus  0  March 9th, 2013 10:11 AM 
solving a limit involving tangent  Math4dummy  Calculus  2  February 14th, 2012 11:24 AM 
Indeterminate limit involving an impossible integral  Etyucan  Calculus  2  October 25th, 2011 08:22 PM 
Right hand limit involving 'e' and 'sine'  Melchoire  Calculus  1  September 29th, 2009 05:42 PM 