What Is The Factorial Of 1/2? SURPRISING (1/2)! = (√π)/2
1,718
by Super User, 4 years ago
The calculator result is not an error, and in this video I explain how the factorial can be extended beyond the whole numbers for all real numbers by the gamma function. Once we extend the factorial function beyond whole numbers, you can see why the factorial of onehalf is equal to the square root of pi divided by 2.
BohrMollerup theorem
http://en.wikipedia.org/wiki/Bohr%E2%80%93Mollerup_theorem
Applications
https://www.math.washington.edu/~morrow/336_10/papers/joel.pdf
Numerical computation
http://www.rskey.org/CMS/index.php/thelibrary/11
Alternative ways to extend the factorial function
http://www.luschny.de/math/factorial/hadamard/HadamardsGammaFunctionMJ.html
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