[tex]
\begin{displaymath}
\frac{a^2 - b^2}{a + b} = a - b
\end{displaymath}
[/tex]

[tex]
\begin{displaymath}
\mathop{\mathrm{corr}}(X,Y)=
\frac{\displaystyle
\sum_{i=1}^n(x_i-\overline x)
(y_i-\overline y)}
{\displaystyle\biggl[
\sum_{i=1}^n(x_i-\overline x)^2
\sum_{i=1}^n(y_i-\overline y)^2
\biggr]^{1/2}}
\end{displaymath}
[/tex]

[tex]
\begin{displaymath}
I(z) = \sin( \frac{\pi}{2} z^2 ) \sum_{n=0}^\infty
    \frac{ (-1)^n \pi^{2n} }{1 \cdot 3 
    \cdots (4n + 1) } z^{4n + 1}
    -\cos( \frac{\pi}{2} z^2 ) \sum_{n=0}^\infty
    \frac{ (-1)^n \pi^{2n + 1} }{1 \cdot 3 
    \cdots (4n + 3) } z^{4n + 3}
\end{displaymath}
[/tex]

[tex]
\psset{unit=0.5cm}
\begin{pspicture}(-4,-0.5)(4,8)
\psgrid[subgriddiv=0,griddots=5,
   gridlabels=7pt](-4,-0.5)(4,8)
\psline[linewidth=1pt]{->}(-4,0)(+4,0)
\psline[linewidth=1pt]{->}(0,-0.5)(0,8)
\psplot[plotstyle=curve,
   linewidth=0.5pt]{-4}{0.9}{10 x exp}
\rput[l](1,7.5){$10^x$}
\psplot[plotstyle=curve,linecolor=red,
   linewidth=0.5pt]{-4}{3}{2 x exp}
\rput[l](2.2,7.5){\color{blue}$e^x$}
\psplot[plotstyle=curve,linecolor=blue,
   linewidth=0.5pt]{-4}{2.05}{2.7183 x exp}
\rput[l](3.2,7.5){\color{red}$2^x$}
\rput(4,8.5){\color{white}change\normalcolor}
\rput(-4,-1){\color{white}bounding box\normalcolor}
\end{pspicture}
[/tex]

    \documentclass[10pt]{article}
    \usepackage{amsmath}
    \usepackage{amsfonts}
    \usepackage{amssymb}
    \usepackage{pst-plot}
    \usepackage{color}
    \pagestyle{empty}
    \begin{document}
     \mathbf{\hat{q}}_i = \frac{1}{h_i} \sum_{j=1}^{3} \mathbf{\hat{x}}_j \frac{\partial x_j}{\partial q_i}
    \end{document}