Product of a serie

  • Thread starter oscaralive
  • Start date
  • #1
oscaralive
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Hi all,
anyone knows how to compute the following serie?

\prod_{i=1}^{a}(a-i+1)^(a-i+1)

Many thanks in advance!
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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hi oscaralive! :smile:

(try using the X2 icon just above the Reply box :wink:)

isn't that just 11223344…aa

why not leave it as it is? :confused:

(or you could write it as (a!)a over something)
 
  • #3
oscaralive
5
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Because i'm trying to find an upper bound to define the complexity of an algorithm....and I cannot put it that way...it would be great to find an appropriate upper bound to this product

Thanks
 
  • #4
tiny-tim
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well, the log would be ∑nlogn … does that help? :smile:
 
  • #5
oscaralive
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In fact, I come from the log serie...

[tex]\sum_{i=1}^{a}(a-i+1)log(a-i+1)[/tex]

[tex]\sum_{i=1}^{a}log((a-i+1)^{(a-i+1)})[/tex]

[tex]log(\prod_{i=1}^{a}{(a-i+1)}^{(a-i+1)})[/tex]
which now has been transformed to the product...

thanks,
 
Last edited:
  • #6
tiny-tim
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i was wondering whether it would be close to ∫ xlogx dx
 
  • #7
oscaralive
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I'm stuck here :(
 

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