Show inline math as if it were display math (and vice versa)

Question

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

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

vs.

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

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 if they were in display mode ?

The inverse -- how to display things in display mode as if they were in inline mode -- is also of interest.

Answer 1

There are two separate aspects to your question, which can be addressed separately:

1. How to control the size of the integral, sum and product symbols

2. How to control the placement of the limits of integration, summation, and multiplication, namely side-set or above/below.

Default settings

The default settings, with the amsmath package loaded, are

• Inline math

  • Small symbol size;
  • Limits are side-set for all operators;
  • The sumlimits and intlimits options of amsmath do not affect the placement of limits in inline math.

• Display math

  • Large symbol size. See Tables 72 through 83 in the Comprehensive LaTeX Symbol List for the names of these 'large' or, more precisely, Variable-sized Math Operators;

  • For \int-type symbols, the limits are side-set unless amsmath was loaded with the option intlimits.

    The integral symbols are treated separately presumably because they are generally taller than the other variable-sized symbols.

  • For \sum, \prod, \coprod, etc the limits are set above and below the operator, except when the amsmath was loaded with the option nosumlimits.

    The sumlimits and nosumlimits options and the \limits and \nolimits commands affect the appearance not only of sum-type symbols but of \prod,\coprod, \bigcup and \bigcap, etc. as well.

Custom settings

• To control the size of the symbol, one writes before the command generating the symbol

  • \textstyle for small symbols;
  • \displaystyle for large symbols; .
  • the declarations \textstyle and \displaystyle may also affect the behavior of subsequent commands in the current math-mode environment, as observed by @HaraldHancheOlsen.

• To control the placement of the limits, one writes after the command generating the symbol

  • \nolimits for side-set limits;
  • \limits for limits set above and below.

These possibilities are illustrated in the table below:

---

The table was produced by the following code:

\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}

---

Personal comments

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.
• When in inline math mode, it's frequently not even necessary to indicate the full set of limits of a summation or multiplication. Expressions such as \sum_i or \prod_j are usually just fine. You may even be able to get away with omitting the i and j indices of summation/multiplication.
• Using the \displaystyle command (to force the creation of large symbols) while in inline math mode is an even worse idea than using \limits.

Answer 2

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.

Answer 3

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

$\lim\limits_{n\to\infty}f(x)$

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.

Answer 4

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.