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 May 29th, 2019, 10:23 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 721 Thanks: 97 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: 1,838 Thanks: 653 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 Thanks from topsquark and idontknow May 29th, 2019, 11:06 PM   #3
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Quote:
 Originally Posted by idontknow Why gamma(1/2) is $\displaystyle 1/2 \cdot sqrt(\pi)$?
It isn't. May 30th, 2019, 02:46 AM   #4
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Quote:
 Originally Posted by idontknow 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]?
The factorial function and the gamma function are closely related. Basically:
$\displaystyle \Gamma (n) = (n - 1)!$. 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. Tags explanation, factorial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post sadmath Geometry 8 September 13th, 2015 06:24 AM daivinhtran Algebra 5 July 24th, 2011 11:54 AM ranna Calculus 11 February 1st, 2011 09:34 PM mattman059 Linear Algebra 2 March 6th, 2009 07:24 AM rain Real Analysis 3 December 31st, 1969 04:00 PM

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