%%
%% The LaTeX Companion, 2ed (second printing August 2004)
%%
%% Example 8-2-9 on page 474.
%%
%% Copyright (C) 2004 Frank Mittelbach, Michel Goossens,
%%    Johannes Braams, David Carlisle, and Chris Rowley
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
%%
%% See http://www.latex-project.org/lppl.txt for details.
%%

\documentclass{ttctexamargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{330.59894pt}

\StartShownPreambleCommands
\usepackage{amsmath}
\newcommand\relphantom[1]{\mathrel{\phantom{#1}}}
\newcommand\ve{\varepsilon}  \newcommand\tve{t_{\varepsilon}}
\newcommand\vf{\varphi}      \newcommand\yvf{y_{\varphi}}
\newcommand\bfE{\mathbf{E}}
\StopShownPreambleCommands
\begin{document}
\begin{equation} \begin{split}
  f_{h, \ve}(x, y)
    &= \ve \bfE_{x, y} \int_0^{\tve} L_{x, \yvf(\ve u)} \vf(x) \,du  \\
    &= h \int L_{x, z} \vf(x) \rho_x(dz)                             \\
    &\relphantom{=} {} + h \biggl[
       \frac{1}{\tve}
       \biggl( \bfE_{y} \int_0^{\tve}  L_{x, y^x(s)} \vf(x) \,ds
               - \tve \int L_{x, z} \vf(x) \rho_x(dz)      \biggr) + \\
    &\relphantom{=} \phantom{{} + h \biggl[ }
       \frac{1}{\tve}
       \biggl( \bfE_{y} \int_0^{\tve}  L_{x, y^x(s)} \vf(x) \,ds
               - \bfE_{x, y} \int_0^{\tve} L_{x, \yvf(\ve s)}
                                            \vf(x) \,ds    \biggr) \biggr]
\end{split} \end{equation}
\end{document}