Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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## #1 2013-12-17 09:06:21

calculator
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### Factorials

My question is how do you find the factorial of any number?  I already know how to find it with counting numbers, but how about negative numbers, or decimals?(I know -0.5!=√π, but it doesn't help with (7/9)!)

## #2 2013-12-17 09:10:37

zetafunc.
Guest

### Re: Factorials

We can use the gamma function to extend the definition of the factorial function to real and complex arguments.

The gamma function isn't defined for negative integers. It is defined for decimals though, but in general, most of them aren't expressible in terms of known constants.

## #3 2013-12-17 09:12:06

anonimnystefy
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### Re: Factorials

Hi calculator

You can use the fact that:

and numerically integrate.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #4 2013-12-17 09:17:52

calculator
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### Re: Factorials

I already know that, but I don't know what ∫ is.

## #5 2013-12-17 11:35:47

bobbym

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### Re: Factorials

Hi;

What kind of calculator are you using? How many digits do you want the answers to be? Are you looking to calculate it? Then we would use series and recurrence relations. If you are trying understand it then the integral which is the definition is purely formal. You would need to numerically integrate to get any practical answer.

Also, remember that for negative integers the gamma function is undefined.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #6 2013-12-19 01:13:38

zetafunc.
Guest

### Re: Factorials

#### calculator wrote:

I already know that, but I don't know what ∫ is.

Have you studied any calculus?