### 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`.

(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