\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}