How to write this equation in publication?

Question

I have the equation in the twocolumn view

\documentclass[twocolumn]{article}
\usepackage{amsmath}
\begin{document}   

\begin{equation}
\begin{aligned}  
X(m) &= \frac{b-a}{N} \sum_{k=1}^{N} e^{-i2\pi (k-1)(m-1)/N} x(a + (b-a)\frac{k-1}{N}) \\ 
&= \frac{b-a}{N} \sum_{k=1}^{N} e^{-i2\pi (a + (b-a)\frac{k-1}{N})*\frac{m-1}{b-a}} \\
& x(a + (b-a)\frac{k-1}{N})e^{i2\pi a \frac{m-1}{b-a}} \\
& \xrightarrow{ N\to\infty } \int_{a}^{b} e^{-2\pi t \frac{m-1}{b-a}} x(t) dt\\
& e^{i2\pi a \frac{m-1}{b-a}} Qx(\frac{m-1}{b-a}). 
\end{aligned}
\end{equation}
\end{document}

Output

enter image description here

How would you present this equation in a twocolumn view?

Please don't just include snippets but a minimal code that can be typeset, from \documentclass{...} to \end{document}, removing the unnecessary code. — Alenanno, Oct 18 '13 at 14:55
Are you saying that you don't like how it looks and you would want suggestions on how to have it look better? — karlkoeller, Oct 18 '13 at 15:03
Don't nest align and equation environments. Both enter math-mode on their own, see this related question. — Qrrbrbirlbel, Oct 18 '13 at 15:03
@karlkoeller Yes. I have also thought to split in two. Now, it looks quite a messy. — Léo Léopold Hertz 준영, Oct 18 '13 at 15:07
So is the question that the top line is too long - what to do about it? re Brackets, you can use \left( and \right) to automate the sizing nicely — Chris H, Oct 18 '13 at 15:11
Could you show the equation without splitting first to let me know where the exact place I have to break the equation? — kiss my armpit, Oct 18 '13 at 15:12
It looks too wide to just tighten with some negative spaces (and will get wider with the right size brackets). I would say the best option is to have a full-width equation. — Chris H, Oct 18 '13 at 15:14
I splitted the other question about brackets here: http://tex.stackexchange.com/questions/139445/automatically-size-the-brackets-by-left-and-right to concentrate here only to the layout. @ChrisH — Léo Léopold Hertz 준영, Oct 18 '13 at 15:21
@Masi Use a_{k} instead of a+(b-a)\frac{k-1}{N}, to begin with. — egreg, Oct 18 '13 at 15:36
@egreg I was going to suggest that. I will also add that there should be larger parentheses around \frac{m-1}{b-a}. — Dan, Oct 18 '13 at 16:55

score 11 · Accepted Answer · edited Jun 04 '17 at 19:15

11

You should be using split not align inside equation. Introducing new variables for large repeating expressions and shifting your indexing by one will reduce the size of the equation. Finally I introduce an eqbreak command to shift a split expression:

Sample output

\documentclass[twocolumn]{article}
\usepackage{amsmath, amsfonts, amssymb, textcomp}

\newcommand{\eqbreak}[1][2]{\\&\hskip#1em}

\begin{document}   

\begin{equation}
  \begin{split}  
    X(m+1)
    &= \frac{b-a}N \sum_{k=0}^{N-1} e^{-i2\pi km/N}\,  x(a_k) \\
    &= \frac{b-a}N \sum_{k=0}^{N-1} e^{-i2\pi a_km/(b-a)} \eqbreak[6]
    \times x(a_k)\,e^{i2\pi a m/(b-a)} \\
    &\xrightarrow{N\to\infty} e^{i2\pi a m/(b-a)} \,Qx\Bigl(\frac
    m{b-a}\Bigr),
  \end{split}
\end{equation}
where \( a_k = a + (b-a)k/N \).
\end{document}

edited Jun 04 '17 at 19:15

Mico

506,678

answered Oct 18 '13 at 15:46

Andrew Swann

95,762

As I just told to Marienplatz, I'm not sure that \times is the right symbol to use... – karlkoeller Oct 18 '13 at 15:47
1

@karlkoeller An alternative would be \cdot, but it depends on the wider context. – Andrew Swann Oct 18 '13 at 15:49
@Marienplatz There is no integral in the poster's example, nor is Qx explained. – Andrew Swann Oct 18 '13 at 15:52
I would go with \cdot... Anyway, as a mathematician, I would say that this is the only answer that looks good, IMHO. +1. – karlkoeller Oct 18 '13 at 15:59
@AndrewSwann Can you please give your feedback here about applying your \eqbreak in Tables http://tex.stackexchange.com/a/324097/13173 I am just using \aligned at the moment and cannot understand possible complications of not using \begin{equation}\begin{split}...\end{split}\end{equation} there. – Léo Léopold Hertz 준영 Aug 10 '16 at 12:05
1

@Masi I will comment on that question - you are missing alignment points. – Andrew Swann Aug 10 '16 at 12:47
@AndrewSwann Here is more simpler thread just using your Math in Table: http://tex.stackexchange.com/a/324191/13173 You can also propose an answer there and/or comment. – Léo Léopold Hertz 준영 Aug 10 '16 at 12:58

score 3 · Answer 2 · edited Jun 04 '17 at 19:17

Just for fun!

\documentclass{article}
\usepackage[a4paper,margin=2cm,twocolumn]{geometry}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{split}  
X(m) 
&=
\!
\begin{multlined}[t]
    \frac{b-a}{N} \sum_{k=1}^{N} \Bigg[  x\left(a + \frac{k-1}{N}(b-a)\right)\\
    \times e^{-\frac{2\pi i (k-1)(m-1)}{N}} \Bigg]
\end{multlined}\\ 
&=
\!
\begin{multlined}[t]
    \frac{b-a}{N} \sum_{k=1}^{N}\Bigg[ x\left(a + \frac{k-1}{N}(b-a)\right) \\
    \times e^{2\pi i a \frac{m-1}{b-a}}\\
    \times e^{-2\pi i \left(a + \frac{k-1}{N}(b-a)\right)\times \frac{m-1}{b-a}}\Bigg]
\end{multlined}\\
& \xrightarrow{ N\to\infty }
\!
\begin{multlined}[t] 
    e^{2\pi i a \frac{m-1}{b-a}} \\
    \times \int_{a}^{b} e^{2\pi i a \frac{m-1}{b-a}} Qx\left(\frac{m-1}{b-a}\right).
\end{multlined}
\end{split}
\end{equation}
\end{document}

enter image description here

I'm not sure that \times is the right symbol to use... – karlkoeller Oct 18 '13 at 15:45 — karlkoeller, Oct 18 '13 at 15:45

Mico · Answer 3 · 2017-06-04T19:16:31.863

I would propose you split the first two lines at a reasonably natural point. I would use explicit sizing instructions for the parentheses, and use \exp(...) expressions.

enter image description here

\documentclass[twocolumn]{article}
\usepackage{amsmath, amsfonts, amssymb, textcomp}
\begin{document}
\begin{align}
&X(m) \notag\\
&= \frac{b-a}{N} \sum_{k=1}^{N} \exp\bigl(-i2\pi (k-1)(m-1)/N\bigr) \notag\\
&\qquad  \times x\Bigl[a + (b-a)\frac{k-1}{N}\Bigr] \\
&= \frac{b-a}{N} \sum_{k=1}^{N} \exp\Bigl[-i2\pi \Bigl(a + (b-a)\frac{k-1}{N}\Bigr)
 \frac{m-1}{b-a}\Bigr] \notag \\
&\qquad  \times x\Bigl(a + (b-a)\frac{k-1}{N}\Bigr) 
        \exp\Bigl(i2\pi a \frac{m-1}{b-a}\Bigr) \\
& \xrightarrow{ N\to\infty } \exp\Bigl(i2\pi a \frac{m-1}{b-a}\Bigr) 
Qx\Bigl(\frac{m-1}{b-a}\Bigr)\,.
\end{align}
\end{document}

How to write this equation in publication?

3 Answers3

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