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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)

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}

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}



newcommanddiff{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 xdiff 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 xdiff 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}

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}