Derivate of Factorial

[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 continous derivative, so the discrete derivative is simple to formulate from this basis.



f(x) = x!




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



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



x_1-x_0=1





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



substituting the general x for



x_0



and x+1 for



x_1



we get



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



= x! * (x+1-1)
= x!*x
= x^2 * (x-1)!



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.