%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-2-28 on page II-147 in "breqn --- Automatic line breaking in math displays".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See
https://www.latex-project.org/lppl.txt for details.
%%
\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{330.59894pt}
% Shorten the vertical size of the example ...
\AtBeginDocument{%
\setlength\abovedisplayskip{.2\abovedisplayskip}%
\setlength\belowdisplayskip{.2\belowdisplayskip}%
}
%StartShownPreambleCommands
\usepackage{breqn}
\newcommand\ve{\varepsilon} \newcommand\tve{t_{\varepsilon}}
\newcommand\vf{\varphi} \newcommand\yvf{y_{\varphi}}
\newcommand\bfE{\mathbf{E}}
%StopShownPreambleCommands
\begin{document}
\begin{dmath}
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) + 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)
+ \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{dmath}
\end{document}
