Omnimaga

General Discussion => Other Discussions => Math and Science => Topic started by: squidgetx on February 23, 2011, 07:46:39 pm

Title: 0.5!
Post by: squidgetx on February 23, 2011, 07:46:39 pm

So according to our trusty calculators...

Code: (that's a factorial symbol!) [Select]

              __
(1/2)!=(1/2)\/pi
              __
(3/2)!=(3/4)\/pi
               __
(5/2)!=(15/8)\/pi
                 __
(7/2)!=(105/16)\/pi
                 __
(9/2)!=(945/32)\/pi
Now, my question is...Why?

Title: Re: 0.5!
Post by: Michael_Lee on February 23, 2011, 08:03:02 pm

That is bizarre.

I don't really understand how taking a factorial of a fraction makes sense, though.

Title: Re: 0.5!
Post by: Juju on February 23, 2011, 08:11:38 pm

Yeah, the factorial function only allows multiples of 1/2 or 1/4, I don't remember... And I dunno why.

Also, that factorial+square root of pi thing is weird. I want a proof.

Title: Re: 0.5!
Post by: program4 on February 23, 2011, 08:39:12 pm

http://en.wikipedia.org/wiki/Gamma_function#Alternative_definitions

http://en.wikipedia.org/wiki/Gamma_function#General

I'm not very knowledgeable in this subject, but Wikipedia might help here.

Title: Re: 0.5!
Post by: squidgetx on February 23, 2011, 08:49:01 pm

Yeah, apparently it has to do with something called the Riemann Zeta Function, which also plays a part in a proof that shows that 1+2+3+...(to infinity)=-1/12 O.o

Title: Re: 0.5!
Post by: Xeda112358 on February 23, 2011, 09:11:48 pm

>_>/me hears you liek Riemann Zeta functions?

If you are looking into taking factorials of fractions, you will want to look into the gamma function... which has ties with the Riemann Zeta function :D

To be honest, I never noticed that the calc returned results for those fractions :D
Hmm...
1
1*3
1*3*5
1*3*5*7
1*3*5*7*9
...