What is the first derivative, and the integral of x!?
1 Answer
May 4, 2017
The factorial function is only defined for integer values, and as such it is undefined for
Having said that the factorial function can be extended to
Gamma(z) = int_o^oo x^(z-1)e^-x \ dx
Along with the relationship:
n! = Gamma(n+1) \ \ \ AA n in NN
The graph of the Gamma function is as follows:
graph{x! [-10, 10, -5, 5]}
And the derivative of the Gamma function is obtained from the polygamma function
psi(z) = (Gamma'(z))/(Gamma(z))
I am not sure what the integral of the Gamma function is - perhaps another member could add details.
