# One-Half Derivative

1. Jan 25, 2008

### Feldoh

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
$$\frac{d^{a}y}{dx^{a}} x^n= \frac{(n!)x^{(n-a)}}{(n-a)!}$$

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. Jan 25, 2008

### LukeD

3. Jan 28, 2008

### Feldoh

Thanks! However once again I seem to be stuck as to how so apply the gamma function.

Specifically this is mentioned:

$$(n+\frac{1}{2})! = \sqrt{\pi} \prod_{k=0}^n \frac{2k+1}{2}$$

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
4. Jan 29, 2008

### Hurkyl

Staff Emeritus
Some buzzwords:

fractional derivative
fractional integral
fractional calculus