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Offline squidgetx

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0.5!
« 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?
« Last Edit: February 23, 2011, 07:48:49 pm by squidgetx »
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Offline Michael_Lee

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Re: 0.5!
« Reply #1 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.
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Offline Juju

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Re: 0.5!
« Reply #2 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.
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Offline program4

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Re: 0.5!
« Reply #3 on: February 23, 2011, 08:39:12 pm »
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Offline squidgetx

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Re: 0.5!
« Reply #4 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
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Offline Xeda112358

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Re: 0.5!
« Reply #5 on: February 23, 2011, 09:11:48 pm »
>_>
* Xeda112358 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
...
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