February 17th, 2013, 03:05 AM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  int(1/n^n) evaluation
Evaluate to many digits using fast accelerations of this integral. Just an easy challenge to our members. 
February 17th, 2013, 04:25 AM  #2  
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: int(1/n^n) evaluation Quote:
 
February 17th, 2013, 04:39 AM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: int(1/n^n) evaluation
@zaidalyafey : I was posted the integral wrong, I edited it so beware of your quoted text! Quote:
 
February 17th, 2013, 07:23 PM  #4  
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: int(1/n^n) evaluation Quote:
 
February 18th, 2013, 01:30 AM  #5  
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: int(1/n^n) evaluation Quote:
http://www.scribd.com/JJacquelin/documents .  
February 18th, 2013, 01:53 AM  #6 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: int(1/n^n) evaluation
Yes, JJacquelin, this is sophomores dream function. The integration can be accelerated through a discrete sum with the same function but with limits 1 to infinity. But still, the accelerated convergence is slow. We need n+1 terms to calculate n digits. Any idea how to again accelerate the sum so that we have a rapid convergence to the original value. I am thinking about Kummers transform...


Tags 
evaluation, int1 or nn 
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