Is there a way to find the derivative, or antiderivative for that matter, of x!. Or is there a special function for that or something?
In that case you can take the discrete-space derivative.Originally posted by lethe
well, the factorial is only defined on the natural numbers, and there is no sensible way to take a derivative of any function on the naturals.
yup. check 1/2! it should be √πOriginally posted by climbhi
Is it perhaps just picking the values off the Gamma function?
Well actually according to my calculator it is (√π)/2, is this actually what it should be?Originally posted by lethe
yup. check 1/2! it should be √π
umm... yeah, i guess so. oops. i guess i meant to say that Γ(1/2) = √π which implies that (1/2)! = Γ(3/2) = (1/2)Γ(1/2) = 1/2√π. OKOriginally posted by climbhi
Well actually according to my calculator it is (√π)/2, is this actually what it should be?
I don't follow this step. By Hurkyl's given definition of what the Gamma function is I don't see how you can take the 1/2 outside. Am I missing something, how does that work?Originally posted by lethe
Γ(3/2) = (1/2)Γ(1/2)