summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/guide-to-latex/exercises/chap7/exer7-8.tex
blob: b163e13ded6acb26550c596c499505101d34f932 (plain)
1
2
3
4
5
6
7
8
9
10
\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}