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February 17th, 2013, 02:05 AM   #1
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int(1/n^n) evaluation

Evaluate to many digits using fast accelerations of this integral.

Just an easy challenge to our members.
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February 17th, 2013, 03:25 AM   #2
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Re: int(1/n^n) evaluation

Quote:
Originally Posted by mathbalarka
Evaluate to many digits using fast accelerations of this integral.

Just an easy challenge our members.
What is fast acceleration
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February 17th, 2013, 03:39 AM   #3
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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!

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What is fast acceleration
Never heard of sequence accelerations?
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February 17th, 2013, 06:23 PM   #4
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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 ...
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February 18th, 2013, 12:30 AM   #5
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Re: int(1/n^n) evaluation

Quote:
Originally Posted by mathbalarka
Evaluate 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
.
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February 18th, 2013, 12:53 AM   #6
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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...
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