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A formula of the product of the first n integers?

  1. Sep 18, 2006 #1

    quasar987

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    I'm sure it exists, and it'd help me to have it. Thx!
     
  2. jcsd
  3. Sep 18, 2006 #2

    AKG

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    n!

    .......................
     
  4. Sep 18, 2006 #3

    quasar987

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    No no, like there's n(n+1)/2 for the sum of the first n integers. Is there an equivalent formula for the product?
     
  5. Sep 18, 2006 #4
    I want to say no since if there was we would probably use that instead of n! everywhere, but there's stirling's approximation to n!.
     
    Last edited: Sep 18, 2006
  6. Sep 18, 2006 #5

    quasar987

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    You're probably right.
     
  7. Sep 19, 2006 #6

    CRGreathouse

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    Stirling's formula gives a good approximation. I prefer to use Gosper's reformulation of same.
     
  8. Sep 19, 2006 #7
    Well, there's always the integral form of the factorial function; although I doubt it's what you're looking for:

    [tex]n! = \Gamma(n+1) = \int_0^{\infty} e^{-t} t^n dt[/tex]
     
  9. Sep 19, 2006 #8
    it's n(n+1)/2 if you start at 1 and n(n-1)/2 if you start at zero if I recall...
     
  10. Sep 19, 2006 #9

    CRGreathouse

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    I think you mean n and n-1, respectively, if you're talking about sums. Obviously adding in 0 has no effect.
     
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