Can n! ever be negative?

  1. If yes, then for what values of n?
     
  2. jcsd
  3. We usually only define ##n!## for natural numbers ##n##. Then ##n!## can never be negative.

    There is however a very natural extension of the factorial, this is called the Pi function (which is just a translation of the Gamma function). This can indeed become negative as you can see from the graph: http://en.wikipedia.org/wiki/Gamma_function
     
    1 person likes this.
  4. lurflurf

    lurflurf 2,326
    Homework Helper

    If we extend the domain we can have negative numbers for example
    -1~(-3.74768264672741260139148848269149969586163939513235551205229915)!
    -1~(-3.45702473822080062303945414765117954323659790903378442096479450)!
     
  5. THAT is what I wanted to see. Thank you very much Sir.
     
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