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#1 2013-12-16 10:06:21

calculator
Member
Registered: 2013-11-06
Posts: 3

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)!)

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#2 2013-12-16 10:10:37

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 2013-12-16 10:12:06

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Factorials

Hi calculator

You can use the fact that:

and numerically integrate.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2013-12-16 10:17:52

calculator
Member
Registered: 2013-11-06
Posts: 3

Re: Factorials

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

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#5 2013-12-16 12:35:47

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,935

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#6 2013-12-18 02:13:38

zetafunc.
Guest

Re: Factorials

calculator wrote:

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

Have you studied any calculus?