What is the Gamma Function and Its Significance in Mathematics?

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[tex]\Gamma(n)=\int_0^\infty\,t^{n-1}e^{-t}dn[/tex]

What is it and what does it mean? Thanks.
 
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I believe that you are trying to write the definition of the Gamma functions but. the integrations should be over the parameter t not n. The Gamma functions is the generalization of the factorial form n! for non integral values of n.
 
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