\section{PSI Psi Function}

\subsection{Usage}

Computes the psi function for real arguments.  The \verb|psi|
function takes only a single argument
\begin{verbatim}
  y = psi(x)
\end{verbatim}
where \verb|x| is either a \verb|float| or \verb|double| array.  The output
vector \verb|y| is the same size (and type) as \verb|x|.
\subsection{Function Internals}

The psi function is defined as
\[
  \frac{d}{dx} \ln \gamma(x)
\]
and for integer arguments, is equivalent to the factorial function.
\subsection{Example}

Here is a plot of the psi function over the range \verb|[-5,5]|.
\begin{verbatim}
--> x = linspace(-5,5);
--> y = psi(x);
--> plot(x,y); xlabel('x'); ylabel('psi(x)');

\end{verbatim}
which results in the following plot.


\centerline{\includegraphics[width=8cm]{psi1}}

