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I'm very familiar with how symbols display differently in inline mode (with $) vs. how display math shows them (with \[ or $$). Two examples would be with limits

$\lim_{n\righarrow \infty}f(x)$

vs.

\[\lim_{n\righarrow \infty}f(x)\]

and with sums

$\sum_{n=1}^{x} n^2$

vs.

\[\sum_{n=1}^{x} n^2\]

My Question is:

How do you display these things in inline mode (with all the nice inline formatting) as though they were in display mode ?

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3  
For reference on the use of \[...\] or $$...$$, see: tex.stackexchange.com/questions/503/why-is-preferable-to –  Werner Oct 26 '11 at 20:58
1  
If the effect you want is only to have the limits look like \displaystyle (but not the larger size) you might want to rephrase the question...in that case you might want to look at \limits. –  Yossi Farjoun Oct 26 '11 at 21:00
    
Related question: Sums in math mode: how to display index under the sigma sign? –  Werner Oct 26 '11 at 21:03

4 Answers 4

up vote 74 down vote accepted

I think there are two separate aspects to your question:

  • How does one control the size of integral, sum and product symbols?

  • How does one control the placement of the limits of integration, summation, and multiplication: side-set vs. below/above?

These two aspects can be addressed separately.

  • To control the size of the operators explicitly, one writes either \textstyle for small symbols or \displaystyle for large symbols, before the command that generates the symbol.
    • Side remark, inspired by an observation by @HaraldHancheOlsen: In addition to influencing the size of the operators created by the commands \sum, \prod, etc, the declarations \textstyle and \displaystyle may also affect the behavior of other subsequent commands in the current math-mode environment.
  • To control the placement of the limits, one writes either \nolimits (for side-set limits) or \limits (for limits set below&above the symbol) after the command that generates the symbol.

The possibilities are illustrated in the table below.

The default settings in LaTeX are (I'm assuming the amsmath package is loaded too):

  • Inline math: Small operator symbols;
    • Limits side-set for all operators;
    • Note: Setting the options sumlimits and intlimits when loading the amsmath package does not affect the placement of limits when in inline math.
  • Display math: Large operator symbols;
    • \sum, \prod, \coprod, etc: Limits set above and below operator, unless amsmath was loaded with the option nosumlimits.
      • Note: The sumlimits and nosumlimits options (and the commands \limits and \nolimits) affect not only the appearance of summation symbols in display math mode, but also that of \prod,\coprod, \bigcup and \bigcap, etc. See Tables 57 to 67 of The Comprehensive LaTeX Symbol List for the names of these "large" -- more precisely, "variable-sized" -- math operators. The only group of variable-sized operators that's treated differently is the set of integral symbols (presumably because they're generally already quite a bit taller than the other "large" operators).
    • \int: Limits are set to the side of integral symbol unless amsmath was loaded with the option intlimits.

enter image description here

Here's the code for the preceding table:

\documentclass[letterpaper]{standalone}
\usepackage{array,amsmath,booktabs}
\begin{document}
\Huge
\begin{tabular}{l
        >{$\textstyle}l<{$}     % first math column: text style
        >{$\displaystyle}l<{$}} % second math column: display style
\toprule
Placement of limits & \multicolumn{2}{c}{Size of operators} \\
\cmidrule{2-3}
 & \multicolumn{1}{l}{small:}
 & \multicolumn{1}{l}{large:}\\
 & \multicolumn{1}{l}{\texttt{\textbackslash textstyle}}
 & \multicolumn{1}{l}{\texttt{\textbackslash displaystyle}}\\
\cmidrule[\lightrulewidth]{2-3}
Next to symbol: & \multicolumn{1}{l}{\phantom{\texttt{\textbackslash displaystyle }}}\\ 
\texttt{\textbackslash nolimits} 
         &   \sum\nolimits_{i=1}^N a_i 
         &   \sum\nolimits_{i=1}^N a_i \\[2ex]
         &  \prod\nolimits_{j=0}^J k_j
         &  \prod\nolimits_{j=0}^J k_j \\[2.5ex]
         &   \int\nolimits_{-\infty}^\infty f(x)\,\mathrm{d}x
         &   \int\nolimits_{-\infty}^\infty f(x)\,\mathrm{d}x \\[5ex]
Below \& above symbol:\\[-1ex]
\texttt{\textbackslash limits}
         &   \sum\limits_{i=1}^N a_i 
         &   \sum\limits_{i=1}^N a_i \\[3.5ex]
         &  \prod\limits_{j=0}^J k_j
         &  \prod\limits_{j=0}^J k_j \\[4ex]
         &   \int\limits_{-\infty}^\infty f(x)\,\mathrm{d}x
         &   \int\limits_{-\infty}^\infty f(x)\,\mathrm{d}x \\
\bottomrule
\end{tabular}
\end{document}

Finally, some personal views on the (ab)uses of the \limits and \displaystyle commands when in inline math mode:

  • It's generally not a good idea to use the \limits command when in inline math mode. Otherwise, one is virtually assured of wrecking the appearance of the paragraph where the formula appears.
  • It's frequently not even necessary to indicate the full set of limits of a summation or multiplication when in inline math mode. Expressions such as \sum_i or \prod_j are usually just fine. You may even be able to get away with omitting the subscripts i and j!
  • Using the \displaystyle command (to force the creation of large symbols) while in inline math mode is an even worse idea than using \limits.
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4  
Informative & educative! –  Werner Oct 26 '11 at 23:07
    
I do agree with you. –  night owl Oct 27 '11 at 7:18
2  
Minor nit: You might have made it more clear that \displaystyle and \textstyle do not affect only the following symbol. They are declarations whose effects last until the end of the formula (or group) or until overridden. –  Harald Hanche-Olsen Oct 27 '11 at 16:20
3  
I have found that \displaystyle in inline math is useful when preparing beamer presentations. In an itemized list, sometimes there is a short text (like two words) preceding a formula, and I don't want to waste valuable vertical space on a displayed formula but do want large symbols. Then \displaystyle is appropriate, since the items in a list are visually similar to displays. –  Ryan Reich Feb 14 '12 at 19:47
    
@RyanReich: Good point about Beamer presentations' material often having different requirements than that of "ordinary" inline material. Thus, bullet point stuff can behave very much like display math material -- and hence may need to invoke \displaystyle and/or \limits. –  Mico Feb 14 '12 at 23:12

This is a wonderful question which I am sure many people have asked from time to time. The solution you seek is to use the \displaystyle command within the inline environment as such.

$\displaystyle\sum_{n=1}^{x} n^2$

This will give the nice effect of the starting term being underneath the sigma and the maximum value above while keeping the symbols inline.

I hope that's what you were looking for.

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10  
Interesting how the presentation is done in the 3rd person. –  Werner Oct 26 '11 at 20:55
    
I figured that it would be the most immediately accessible for people quickly looking for an answer :) . –  akdom Oct 26 '11 at 20:58
    
Well, it a wrong answer. –  egreg Oct 26 '11 at 21:00
    
@egreg: The answer isn't wrong....it answers the question exactly. I think that the question is wrong...but that's what down-voting the question is for... –  Yossi Farjoun Oct 26 '11 at 21:33
7  
I have to admit that I don't like the way that the answer is phrased (irrespective of whether or not it is correct). Answering ones own question is absolutely fine, but do it honestly not pretending that you aren't the person who asked the question. –  Loop Space Oct 27 '11 at 6:36

Good typography relies on the balance of all aspects of black and white on the page. Uniformly spaced lines for the ordinary text make for good legibility. That's why some symbols, that in display are rendered with limits above and below, are set with limits on the side when used in in-line formulas.

I too, when I began to use TeX, tried to set limits for sums above and below also in in-line formulas, but I soon realized that it's wrong: two white bands separated that line from the next ones.

For that very reason the symbols for summation and integral are set in two different sizes: a smaller one for in-line formulas, a larger one for displayed formulas that don't have spacing constraints.

Displayed formulas are set using (automatically) \displaystyle, so

$\displaystyle\sum_{n=1}^{x} n^2$

would produce the same symbol used in displayed formulas and set limits above and below. But this will damage the balance of the page beyond repair. A less invasive construction

$\sum\limits_{n=1}^{x} n^2$

and its sibling

$\lim_{n\to\infty}f(x)$

will do less damage to the page, but will nevertheless spoil it.

Such constructions have their use, for examples in tables where TeX would use in-line math mode. But I will never suggest to use them in normal text.

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2  
While true, your answer reads a little patronizing. I think we can treat users of this site as adults. if somebody asks how to do something, we should not assume that they do not know what they are talking about, or at-least should not let our answer show that... :-) –  Yossi Farjoun Oct 26 '11 at 21:32
    
I agree... if you would re-word it to be less condescending (and actually answer the question instead of saying how wrong it is to ask it) I would likely up-vote your answer. –  akdom Oct 26 '11 at 21:39
14  
@YossiFarjoun, while egreg's response is a bit sharp, I don't think it is always a bad idea to question someone's purpose for wanting to achieve a certain look with TeX. As someone who started using LaTeX not too long ago, I must credit my still-improving sense for good typesetting to people who told me that I didn't actually want to do what I said I wanted to do. I would be a poorer TeXer were it not for them. In general, it seems to be a feature of well-designed systems that learning them requires shifting one's approach to problems. –  JohnJamesSmith Oct 26 '11 at 22:08
2  
That's a fantastic new version egreg. Definitely a more complete answer to the question. –  akdom Oct 27 '11 at 23:37
    
Exactly what I needed! Thanks. –  darksky Sep 11 '12 at 13:00

The other answers are excellent, and normally I would not try to change the behavior of inline functions. However, there is one case where I wish inline functions to behave just like displayed functions. That is when I write exams. I am willing to compromise on typesetting for readability. If you put

\everymath{\displaystyle}

in your preamble, every equation will be typeset in that manner, and you don't have to put \displaystyle in every equation. Of course, if you are looking to change just a few equations, then \displaystyle is easy to use.

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