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factorial of a decimal


dstebbins

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When you perform the expression n! (read "n factorial"), you multiply all the positive integers between one and n. They have to be positive, so n>0, but they also have to be integers, so you would think that factorial of a decimal is impossible.

 

However, when I put it into my computer's calculator, I do get a real answer. For example, .01! = 0.99432585119150603713532988870511..., and 2.1! = 2.1976202783924770541835645379483..., so there must be a way to perform a factorial of a decimal.

 

What is it? How do you do that?

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Can't say I understand what a factorial of a non-natural number would mean.

I always understood that the definition was the amount of ways to order n objects and any formula was merely a way of calculating that. And ways to order 2.5 distinct objects doesn't make much sense to me.

 

Although I guess I could have it very backwards.

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Can't say I understand what a factorial of a non-natural number would mean.

I always understood that the definition was the amount of ways to order n objects and any formula was merely a way of calculating that. And ways to order 2.5 distinct objects doesn't make much sense to me.

 

Although I guess I could have it very backwards.

 

No, you are correct- the "factorial" is only defined for positive itegers. What others are saying here is that the "gamma function" has the property that it is identical to the factorial for positive integer values of the argument but is defined for other numbers as well. (It is NOT defined for negative integers because the integral does not exist in that case.)

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  • 15 years later...
  • 5 weeks later...
On 7/6/2023 at 12:22 PM, Gyana Ranjan Nayak said:

This calculation seems to be correct.

Just in case anybody's interested, and because this thread has recently been revived, there's another definition that overlaps with that of a factorial (or gamma function). Namely, the falling and rising factorials.

Although it's a generalisation in a different sense. The variable is not the "n" in n!

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