My solution to small brackets and missing delimiter (. inserted) error

Question

Problem:

\begin{equation}
    \begin{split}
        S_{2(n+1)}^{(1)}=\frac{2}{\Gamma(n+1)}\int_{0}^{G}dxx^{2n+1}[-1+\\
        +n_{1}(\frac{\pi}{\alpha})^{3/2}\sideset{}{'}\sum_{l}e^{-k_{l}^{2}a^{2}/4x^{2}}]
    \end{split}
\end{equation}

First try:

\begin{equation}
    \begin{split}
        S_{2(n+1)}^{(1)}=\frac{2}{\Gamma(n+1)}\int_{0}^{G}dxx^{2n+1}\left[-1+\right.\\
        +n_{1}\left(\frac{\pi}{\alpha}\middle)^{3/2}\sideset{}{'}\sum_{l}e^{-k_{l}^{2}a^{2}/4x^{2}}\right]
    \end{split}
\end{equation}

Bad output

Second try:

\begin{equation}
    \begin{split}
        S_{2(n+1)}^{(1)}=\left\frac{2}{\Gamma(n+1)}\int_{0}^{G}dxx^{2n+1}\right[-1+\\
        +n_{1}\left(\frac{\pi}{\alpha}\middle)^{3/2}\sideset{}{'}\sum_{l}e^{-k_{l}^{2}a^{2}/4x^{2}}\right]
    \end{split}
\end{equation}

Good output, but with missing delimiter (. inserted) error.

My solution:

\begin{equation}
    \begin{split}
        S_{2(n+1)}^{(1)}=\left.\frac{2}{\Gamma(n+1)}\int_{0}^{G}dxx^{2n+1}\right[-1+\\
        +n_{1}\left(\frac{\pi}{\alpha}\middle)^{3/2}\sideset{}{'}\sum_{l}e^{-k_{l}^{2}a^{2}/4x^{2}}\right]
    \end{split}
\end{equation}

I have never seen the use of \left., so I am skeptical. Am I missing a proper way to go around this or is this it? Honestly, when writing the code of "my solution" I could not predict its output.

Thank you

PS: I hope this example, beyond the answers, will help others.

Answer 1

This is how I would recommend doing it. I cleaned up all your \left( and \right) commands and for the square brackets I used \Big[ to get a specific size. Some points to note:

1. It's generally not good practice to repeat plus/minus signs on both lines. For example two minus signs could be mistaken for a plus sign. In your case, you've repeated the plus sign, but avoid this I would say.

2. the d in dx is not a variable. Therefore you should use mathrm{d}. Also it's better to put some thinspace \, between the dx and the x which follows immediately. So write \mathrm{d}x \, x. This separates them slightly and makes it clearer to read.

3. If you add some horizontal space using \hspace on the second line I think the equation looks better. Easier for the eye to see that the second line is a continuation of the first line. If the second line is perfectly aligned with the = sign then it is not so clear.

In addition, I've used & signs to mark the alignment between lines and I've added a small amount of vertical space between the lines using [.5em]. This again just makes it slightly clearer, especially as you have large brackets.

MWE

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
   \begin{split}
        S_{2(n+1)}^{(1)}&=\frac{2}{\Gamma(n+1)}\int_{0}^{G}\mathrm{d}x\,x^{2n+1}\Big[-1\\[.5em]
        &\hspace{1cm}+n_{1}\left(\frac{\pi}{\alpha}\right)^{3/2}\sideset{}{'}\sum_{l}e^{-k_{l}^{2}a^{2}/4x^{2}}\Big]
   \end{split}
\end{equation}
\end{document}

Some additional changes you could make... These are entirely optional but I think it makes the equation read better.

1. Using \frac for your superscript fractions. Again, it is personal choice.

2. Using \exp when you have a very big exponent.

Slightly different MWE

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
   \begin{split}
        S_{2(n+1)}^{(1)}&=\frac{2}{\Gamma(n+1)}\int_{0}^{G}\mathrm{d}x\,x^{2n+1}\Bigg[-1\\[.5em]
        &\hspace{1cm}+n_{1}\left(\frac{\pi}{\alpha}\right)^{\frac{3}{2}}\sideset{}{'}\sum_{l}\exp\left(\frac{-k_l^2 a^2}{4x^2}\right)\Bigg]
   \end{split}
\end{equation}
\end{document}