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One-Half Derivative

  1. Jan 25, 2008 #1
    A few days ago one of my teachers was talking about a half-derivative with basic polynomials and I got bored and tried to figure it out.

    I found that we get
    [tex]\frac{d^{a}y}{dx^{a}} x^n= \frac{(n!)x^{(n-a)}}{(n-a)!}[/tex]

    The problem is when you set a=1/2 I get (n-1/2)! in my denominator and I'm not really sure how to interpret that...
     
    Last edited: Jan 25, 2008
  2. jcsd
  3. Jan 25, 2008 #2
  4. Jan 28, 2008 #3
    Thanks! However once again I seem to be stuck as to how so apply the gamma function.

    Specifically this is mentioned:

    [tex](n+\frac{1}{2})! = \sqrt{\pi} \prod_{k=0}^n \frac{2k+1}{2}[/tex]

    But I'm not really sure how that is derived... Actually the gamma function itself just confuses me.

    Also is there even any use to a half-derivative?
     
    Last edited: Jan 28, 2008
  5. Jan 29, 2008 #4

    Hurkyl

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    Some buzzwords:

    fractional derivative
    fractional integral
    fractional calculus
     
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