alignat align two sums under each other

Question

This

\begin{alignat*}{2}
f(a) &= \lim_{s} \frac{1}{2 z} \int_{-w}^{+e}\int_{-r}^{+t} g(q)\cdot h(q) d x d y  &\\
    &= \lim_{s} \frac{1}{3s} &\Bigg\{  \sum_{w} \int_{-r}^{+t} g(q+e)\cdot h(q) d x d y d x d y &\\
    & &  \sum_{w} \int_{-r}^{+t} g(q)\cdot h(q) d x d y d x d y &\Bigg\} \\ 
\end{alignat*}

Produces this:

Obviously, the space between the fraction and curly bracket is not intended, what I wanted to do was to align the second sum under the first one like it is done here. What is incorrect? (I want to do it with alignat without getting too complex like nested alignemets)

Answer 1

This is a case for split with a nested aligned or multlined environment.

A couple of notes

1. dx should be preceded by a thin space; it's easy to forget it, so I provide a \diff command that adds it automatically;

2. \Bigg is too large and it should be in the \Biggl and \Biggr varieties anyhow; I used \biggl and \biggr;

3. in the aligned solution, there should be a \! before \sum to avoid an unwanted thin space.

\documentclass{article}
\usepackage{amsmath,mathtools}

\newcommand\diff{\mathop{}\!d}

\begin{document}

\begin{equation*}
\begin{split}
f(a)
&= \lim_{s} \frac{1}{2z} \int_{-w}^{+e}\int_{-r}^{+t} g(q)\cdot h(q)\diff x\diff y
\\
&= \lim_{s} \frac{1}{3s} \biggl\{
   \begin{aligned}[t]
     &\!\sum_{w} \int_{-r}^{+t} g(q+e)\cdot h(q) \diff x \diff y \diff x \diff y \\
     &\!\sum_{w} \int_{-r}^{+t} g(q)\cdot h(q) \diff x \diff y \diff x \diff y 
   \biggr\}
   \end{aligned}
\end{split}
\end{equation*}

\begin{equation*}
\begin{split}
f(a)
&= \lim_{s} \frac{1}{2z} \int_{-w}^{+e}\int_{-r}^{+t} g(q)\cdot h(q)\diff x\diff y
\\
&= \lim_{s} \frac{1}{3s} \biggl\{
   \begin{multlined}[t]
     \sum_{w} \int_{-r}^{+t} g(q+e)\cdot h(q) \diff x \diff y \diff x \diff y \\
     \sum_{w} \int_{-r}^{+t} g(q)\cdot h(q) \diff x \diff y \diff x \diff y 
   \biggr\}
   \end{multlined}
\end{split}
\end{equation*}

\end{document}

Answer 2

A combination of an \hphantom{\Bigg\{} and some additional alignment points gives good results:

Notes:

• The alignat*= environment produces as many rl (right/left) pairs as specified in the first parameter and does not insert additional space that the align environment does, so you need to insert the space that is desired between the alignment points (this was not needed in this case).
• The double && ensure that the subsequent columns are also left aligned.

Code

\documentclass{article}
\usepackage{mathtools}% include amsmath

\begin{document}
\begin{alignat*}{4}
f(a) 
    &= \lim_{s} \frac{1}{2 z} &&                    \int_{-w}^{+e}\int_{-r}^{+t} g(q)\cdot h(q) d x d y      & \\
    &= \lim_{s} \frac{1}{3s}  &&           \Bigg\{  \sum_{w} \int_{-r}^{+t} g(q+e)\cdot h(q) d x d y d x d y & \\
    &                         && \hphantom{\Bigg\{} \sum_{w} \int_{-r}^{+t} g(q)\cdot h(q) d x d y d x d y   & \Bigg\} \\ 
\end{alignat*}
\end{document}

Answer 3

A solution with an aligned environment nested in a align*. I also propose a different alignment, and an improvement for the spacing of differential symbols:

    \documentclass{article}
    \usepackage{amsmath}

     \begin{document}

   \begin{align*}
    f(a) &= \lim_{s} \frac{1}{2 z} \int_{-w}^{+e}\int_{-r}^{+t} g(q)\cdot h(q)\, d x\,d y &\\
        &= \lim_{s} \frac{1}{3s}\begin{aligned}[t]\Bigg\{ & \sum_{w} \int_{-r}^{+t} g(q+e)\cdot h(q) \,d x\,d y\,d x\,d y \\
        & \sum_{w} \int_{-r}^{+t} g(q)\cdot h(q) \,d x\, d y \, d x\, d y\, \Bigg\}\end{aligned}
    \end{align*}
    \bigskip

   \begin{align*}
    f(a) &= \lim_{s} \frac{1}{2 z} \int_{-w}^{+e}\int_{-r}^{+t} g(q)\cdot h(q) \,d x\,d y &\\
    &= \lim_{s} \frac{1}{3s}\begin{aligned}[t]\Bigg\{\sum_{w} \int_{-r}^{+t} g(q+e)\cdot h(q) \,d x\,d y\,d x\,d y & \\
   \sum_{w} \int_{-r}^{+t} g(q)\cdot h(q)\,d x\,d y\,d x\,d y &\,\Bigg\}\end{aligned}
    \end{align*}

     \end{document}