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       #Post#: 113--------------------------------------------------
       GAMMA FUNCTION
       By: eba95 Date: July 30, 2010, 6:44 am
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       Gamma Function
       The Gamma function is an amazing
       integral:
       Gamma(x) = INTEGRALt=0 to infinity
       tx-1 e-t dt .
       Using integration by parts, you can
       show that this function satisfies the
       property
       Gamma(x) = (x-1) Gamma(x-1).
       Using Gamma(1)=1, you can
       calculate Gamma(2), Gamma(3),...
       Does this remind you of anything?
       Surprise: the Gamma function
       satisfies Gamma(n) = Factorial(n-1).
       (I would have used the notation "!"
       but you might think I was just
       excited!)
       So you can think of the Gamma
       function as being a continuous form
       of the factorial function. It satisfies
       lots of cool properties; here is just
       one:
       Gamma(1/2) = Sqrt[Pi].
       Presentation Suggestions:
       See if the class can figure out Gamma
       (2), Gamma(3), etc. You may wish to
       assign the integration by parts as a
       homework exercise prior to
       presenting this Fun Fact.
       The Math Behind the Fact:
       The Gamma function is an important
       function in analysis, complex
       analysis, combinatorics, and
       probability.
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