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   Author  Topic: Sum of alternating primes  (Read 842 times)
JocK
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Sum of alternating primes  
« on: Aug 4th, 2007, 9:44am »		 Quote Quote Modify Modify
can you regularise 2 - 3 + 5 - 7 + 11 - 13 + 17 - 19 + 23 - 29 + 31 - 37 + ...   Huh
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.

xy - y = x5 - y4 - y3 = 20; x>0, y>0.
towr
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Re: Sum of alternating primes  
« Reply #1 on: Aug 4th, 2007, 11:27am »		 Quote Quote Modify Modify
What is 'regularising'?
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Wikipedia, Google, Mathworld, Integer sequence DB
Eigenray
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Re: Sum of alternating primes  
« Reply #2 on: Aug 4th, 2007, 9:52pm »		 Quote Quote Modify Modify
For example,
 
1 + 2 + 3 + 4 + ... "=" -1/12,
 
and
 
1*2*3*4*... "=" \sqrt{2\pi},
 
by a naive interpretation of zeta(-1) and zeta'(0), respectively.
« Last Edit: Aug 4th, 2007, 9:59pm by Eigenray » IP Logged
JocK
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Re: Sum of alternating primes  
« Reply #3 on: Aug 5th, 2007, 2:03am »		 Quote Quote Modify Modify
Some more background can be found in:
 
http://en.wikipedia.org/wiki/Divergent_series
 
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.

xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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