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For integer x only, is x! considered a polynomial?

  1. Nov 19, 2008 #1

    tgt

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    For integer x only, is x! considered a polynomial?
     
  2. jcsd
  3. Nov 19, 2008 #2
    Re: x!

    no 4char
     
  4. Nov 19, 2008 #3
    Re: x!

    well,
    x! = x * (x - 1) * (x - 2) * ... * 2 * 1

    And for any integer x! = n where n is some integer.

    So, is an integer a polynomial?
     
  5. Nov 19, 2008 #4

    HallsofIvy

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    Re: x!

    That's a strange response! For any integer, x, x2= n where n is some integer.
    Is an integer a polynomial? No, of course not. But that has nothing at all to do with whether or not x2 is a polynomial, which it is.

    x!, for x a positive integer is not a polynomial but for a very different reason: because it does not satisfy the definition of "polynomial".
     
  6. Nov 19, 2008 #5
    Re: x!

    From Wikipedia:
    A function ƒ of one argument is called a polynomial function if it satisfies

    for all arguments x, where n is a nonnegative integer and a0, a1,a2, ..., an are constant coefficients.

    I think integer fits this definition since n is allowed to be 0, no?
     
  7. Nov 19, 2008 #6

    HallsofIvy

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    Re: x!

    Yes, you can think of the constant function, whether or not it is an integer, as a polynomial. But that still has nothing to do with the question. Surely you are not confusing a function with a value of the function?
     
  8. Nov 19, 2008 #7
    Re: x!

    I would think that is exactly what I am doing. I apologize tgt if I mislead you.
     
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