### Sub- and superscript positioning for operators

The commonest hand-written style for expressions is to place the limit expressions on operators such as `\``sum` and `\``int` physically above and below the operator. In (La)TeX, we write these limit expressions using sub- and superscripts applied to the operator, but they don’t always appear in the “handwritten” way in TeX’s output.

The reason is, that when an expression appears in non-display maths, in running text (and is therefore in TeX `\``textstyle`), placing the limits thus could lead to ragged line spacing (and hence difficult-to-read text). It is therefore common (in `\``textstyle`) to place the limits as one would sub- and superscripts of variables.

This is not universally satisfactory, so the primitive `\``limits` is provided:

>     $\sum\limits_{n=1}^{m} ...$

which will place the limits right above and below the symbol (and be blowed to the typography...).

Contrariwise, you may wish to change the arrangement of the limits when in `\``displaystyle`. For this purpose, there’s a corresponding `\``nolimits`:

>     \[\sum\nolimits_{n=1}^{m} ...\]

which will place the limits as they would be in `\``textstyle`.

Alternatively, one can manipulate the `\``textstyle`/`\``displaystyle` state of the mathematics. To get “`\``limits` placement” in inline maths,

>     $\displaystyle\sum_{n=1}^{m} ...$

and for “`\``nolimits` placement” in display maths, `\``nolimits`:

>     \[\textstyle\sum_{n=1}^{m} ...\]

will serve. Either of these forms may have effects other than on the operator you’re considering, but there are still those who prefer this formulation.

(Note that the macro `\``int` normally has `\``nolimits` built in to its definition. There is an example in the TeXbook to show how odd `\``int``\``limits` looks when typeset.)

This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=limits