Is There a Simple Way to Compute Derivatives for Factorials Beyond the Basics?

[Ebolamonk3y]

Is there a simple neat process to compute derivates for factorials beyond the simple ones...

 

[fourier jr]

I don't understand... can you post the actual problem?

 

[Janitor]

Are you asking about the Gamma function?

If so, this may help:

http://mathworld.wolfram.com/GammaFunction.html

 

[franznietzsche]

Given that the factorial is a discrete function, not a continuous one, there is no continuous derivative, so the discrete derivative is simple to formulate from this basis.

[tex]

f(x) = x!

[/tex]
[tex]

\frac{df}{dx} = \frac{\delta f}{\delta x}
= \frac{f_1-f_0}{x_1-x_0}

[/tex]

Now because f(x) is discrete, the only important values are integers so

[tex]

x_1-x_0=1

[/tex]

[tex]

\frac{df}{dx} = (x_1)! - (x_0)!

[/tex]

substituting the general x for

[tex]

x_0

[/tex]

and x+1 for

[tex]

x_1

[/tex]

we get

[tex]

\frac{df}{dx} = (x+1)! - x!
= (x+1)*x! - x!

[/tex]
[tex]
= x! * (x+1-1)
= x!*x
= x^2 * (x-1)!

[/tex]

There is your discrete derivative for integer values of x, it is the difference between the value of f at x and x+1 in terms of x.


Note: LaTeX friggin hates me.