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The gamma function $\Gamma(x)$ is defined as
\[ \Gamma(x)\equiv\lim_{n\to\infty}\prod_{\nu=0}^{n-1}\frac{n!n^{x-1}}{x+\nu}
	    = \lim_{n\to\infty}\frac{n!n^{x-1}}{x(x+1)(x+2)\cdots(x+n-1)}
	    \equiv\int_0^\infty e^{-t}t^{x-1}\,dt \]
The integral definition is valid only for $x>0$ (2nd Euler integral).
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