How do I adjust the cases?

The space between the lines is too small. How can I adjust it?

$$\tag{12} \left\{ \begin{array}{ll} U_{1}(x) = \sum_{|n| \leq N} A_{n}e^{i\alpha_{n}x} + \sum^{2}_{l = 1}a_{l} \frac{x^{l}}{l!} \\ U^{'}_{1}(x) = \sum_{|n| \leq N} A_{n}i\alpha_{n}e^{i\alpha_{n}x} + \sum^{2}_{l = 1}a_{l} \frac{x^{l - 1}}{(l - 1)!} \end{array} \right. \texttt{where \alpha_{n} = 2n\pi{}}$$

• have you considered using the cases environment? – Bort Oct 22 '16 at 20:21
• Welcome to the site! :) I've modified your code ever so slightly so that it can be hard-wrapped more easily. This is primarily because it displays better on this site (no need to scroll left and right through the code sample block to read everything). Also $\alpha_{n}$ = 2n$\pi{}$ should read $\alpha_{n} = 2n\pi$. You shouldn't hop in and out of math mode around the = and I believe the way you had it would have 2n in typewriter text. If you really want that, it would probably be better style to use \mathtt{} within math mode. – Au101 Oct 22 '16 at 20:25
• In math mode, you can also avoid the need to add {} after commands by using a space instead, this will not affect the output – Au101 Oct 22 '16 at 20:25

Two solutions with a simpler code: one with the dcases environment (displaystyle cases) from mathtools, and the empheq environment. Don't load amsmath: empheq loads mathtools, which loads it.

\documentclass{article}
\usepackage{empheq}

\begin{document}

$$\begin{dcases} U_1(x) = \sum_{|n| \leq N}A_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^l}{l!} \\ U'_1(x) = \sum_{|n| \leq N}A_n i\alpha_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^{l - 1}}{(l - 1)!} \end{dcases} \quad\text{where}\quad \alpha_n = 2n\pi$$

\begin{empheq}[left=\empheqlbrace]{equation}
\begin{aligned}
U_1(x) & = \sum_{|n| \leq N}A_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^l}{l!} \\%[2\jot]
U'_1(x) & = \sum_{|n| \leq N}A_n i\alpha_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^{l - 1}}{(l - 1)!}
\end{aligned}
\end{empheq}

\end{document}


• empheq seems quite a sledgehammer here: \left\{\begin{aligned}...\end{aligned}\right. would do as well. – egreg Oct 22 '16 at 22:26
• @egreg: It was to show another possibility. I don't like to use the pair \left\{ … \right. because it's so easy to forget the \right. and so hard sometimes to find where is this damned error (especially in maths formulae). That said, I find dcases is the best choice. – Bernard Oct 22 '16 at 23:04

Here are some options, including the addition of \displaystyle to stretch out the cases vertically:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

$$\left\{ \begin{array}{ l l } U_1(x) = \sum_{|n| \leq N}A_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^l}{l!} \\ U'_1(x) = \sum_{|n| \leq N}A_n i\alpha_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^{l - 1}}{(l - 1)!} \end{array} \right. \text{where \alpha_n = 2n\pi}$$

$$\left\{\setlength{\arraycolsep}{0pt} \begin{array}{ r l @{\quad} l } U_1(x) &{}= \sum_{|n| \leq N}A_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^l}{l!} \\[2\jot] U'_1(x) &{}= \sum_{|n| \leq N}A_n i\alpha_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^{l - 1}}{(l - 1)!} \end{array} \right. \text{where \alpha_n = 2n\pi}$$

$$\left\{\setlength{\arraycolsep}{0pt} \begin{array}{ r l @{\quad} l } U_1(x) &{}= \displaystyle\sum_{|n| \leq N}A_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^l}{l!} \\[\jot] U'_1(x) &{}= \displaystyle\sum_{|n| \leq N}A_n i\alpha_n e^{i\alpha_n x} + \sum^2_{l=1}a_l \frac{x^{l - 1}}{(l - 1)!} \end{array} \right. \text{where \alpha_n = 2n\pi}$$

\end{document}


Ultimately, since you're using an array to set the cases, you can adjust the vertical spacing using methods from Column and row padding in tables.

• Reconsider your use of a sum where the index runs from 1 to 2. That would just be two terms you could possibly simplify. – Werner Oct 22 '16 at 20:24