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authorKarl Berry <karl@freefriends.org>2009-05-23 00:23:51 +0000
committerKarl Berry <karl@freefriends.org>2009-05-23 00:23:51 +0000
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+\documentclass{article}
+\setlength{\textwidth}{135mm}
+\begin{document}
+\noindent
+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).
+\end{document}