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Factorial function

  1. Apr 12, 2008 #1
    1. The problem statement, all variables and given/known data

    I was just wondering if
    [tex]n!=n(n-1)![/tex]
    is completely general. Does it hold even for non-integer n?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 12, 2008 #2

    rock.freak667

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    Homework Helper

    In general, n! is only for integers.

    (But it is possible to compute nCr for n being negative or a non-integer.)
     
  4. Apr 12, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    How would you define n! for non-integer in order to have it hold?

    The gamma functions, [itex]\Gamma(z)= \int_0^\infty t^{z-1} e^{-t}dt[/itex] has the property that [itex]\Gamma(z)= (z-1)![/itex] for z a positive integer, and is defined for all z except negative integers.
     
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