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May 29th, 2019, 10:23 PM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 541 Thanks: 82  Explanation for factorial !
Why gamma(1/2) is $\displaystyle 1/2 \cdot sqrt(\pi) $? Does $\displaystyle (1/2)!$ make sense or applied in physics? If so , then is (1/2)! the product of all real numbers in interval (0,1]? Last edited by skipjack; May 29th, 2019 at 11:06 PM. 
May 29th, 2019, 11:01 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,826 Thanks: 646 Math Focus: Yet to find out. 
They show up all over the place and it's probably not as mysterious as you think (though the more you look, the more intricate it becomes I suppose). https://en.wikipedia.org/wiki/Gamma_function 
May 29th, 2019, 11:06 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,759 Thanks: 2138  
May 30th, 2019, 02:46 AM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,205 Thanks: 901 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle \Gamma (n) = (n  1)!$. We have $\displaystyle \Gamma (1/2) = \sqrt{ \pi } $ and $\displaystyle (1/2)! = \dfrac{\sqrt{\pi}}{2}$. (1/2)! can't be the product of all real numbers in (0, 1]. That would be....hard to calculate. One definition of the Gamma function where the argument does not need to be an integer is $\displaystyle \Gamma (z) = \int _0^{\infty} e^{z  1} x^z ~ dx$. Here z is, in general, a complex number such that the real part of z is greater than 0. Here's a link to see a graph that includes negative values of z. The Gamma function has many many uses in both Mathematics and Physics. Dan Last edited by topsquark; May 30th, 2019 at 02:54 AM.  

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