(I am currently conceptually wrestling with the Gamma function myself, and your question either has an obvious superficial answer, or I’ve misunderstood it. Probably the latter.)
A function that fills in the gaps between factorials seems useful. There is a simple formula which does just that.
That’s almost what the Gamma function does, but not quite. The Gamma function calculates this:
Here’s its common integral form:
It’s like you’re asking for the factorial of n, and the Gamma function says “Hey, I’ll do you a favor and calculate the factorial of n − 1”, and you’re like “No, that’s okay Gamma function, I really just want the factorial of n”, and the Gamma function is like “No, I want to do this for you”, and then it takes your number, subtracts one, computes the factorial, and hands you back the factorial of n − 1, all beaming and proud of itself for putting in the extra effort, and you have to smile and say thank you.
Can you elaborate on the Gamma function thing?
(I am currently conceptually wrestling with the Gamma function myself, and your question either has an obvious superficial answer, or I’ve misunderstood it. Probably the latter.)
A function that fills in the gaps between factorials seems useful. There is a simple formula which does just that.
That’s almost what the Gamma function does, but not quite. The Gamma function calculates this:
Here’s its common integral form:
It’s like you’re asking for the factorial of n, and the Gamma function says “Hey, I’ll do you a favor and calculate the factorial of n − 1”, and you’re like “No, that’s okay Gamma function, I really just want the factorial of n”, and the Gamma function is like “No, I want to do this for you”, and then it takes your number, subtracts one, computes the factorial, and hands you back the factorial of n − 1, all beaming and proud of itself for putting in the extra effort, and you have to smile and say thank you.
OK, yeah, it was the latter. I see where you’re coming from now.