\section{EI Exponential Integral Function}

\subsection{Usage}

Computes the exponential integral function for real arguments.  The \verb|ei|
function takes only a single argument
\begin{verbatim}
  y = ei(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 ei function is defined by the integral:
\[
  \mathrm{ei}(x) = -\int_{-x}^{\infty} \frac{e^{-t}\,dt}{t}.
\]
\subsection{Example}

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

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


\centerline{\includegraphics[width=8cm]{ei1}}

