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 February 17th, 2013, 02:05 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 $\int_{0}^{1} \frac{1}{z^z} \,\, \mathbb{d}z$ to many digits using fast accelerations of this integral. Just an easy challenge to our members.
February 17th, 2013, 03:25 AM   #2
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Re: int(1/n^n) evaluation

Quote:
 Originally Posted by mathbalarka Evaluate $\int_{1}^{\infty} \frac{1}{z^z} \,\, \mathbb{d}z$ to many digits using fast accelerations of this integral. Just an easy challenge our members.
What is fast acceleration

February 17th, 2013, 03:39 AM   #3
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From: India, West Bengal

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Re: int(1/n^n) evaluation

@zaidalyafey : I was posted the integral wrong, I edited it so beware of your quoted text!

Quote:
 Originally Posted by zaidalyafey What is fast acceleration
Never heard of sequence accelerations?

February 17th, 2013, 06:23 PM   #4
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Joined: Aug 2012
From: Sana'a , Yemen

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Math Focus: Theory of analytic functions
Re: int(1/n^n) evaluation

Quote:
Originally Posted by mathbalarka
@zaidalyafey : I was posted the integral wrong, I edited it so beware of your quoted text!

Quote:
 Originally Posted by zaidalyafey What is fast acceleration
Never heard of sequence accelerations?
I heard about them twice , and you were the source ...

February 18th, 2013, 12:30 AM   #5
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Re: int(1/n^n) evaluation

Quote:
 Originally Posted by mathbalarka Evaluate $\int_{0}^{1} \frac{1}{z^z} \,\, \mathbb{d}z$ to many digits using fast accelerations of this integral. Just an easy challenge to our members.
Yes, it is. Especially with reference to "The Sophomore's Dream Function", (7:4)
http://www.scribd.com/JJacquelin/documents
.

 February 18th, 2013, 12:53 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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