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.

Remember, if you’re declaring a special operator of your own, the amsmath package functions (that you ought to be using) allow you to choose how limits are displayed, at definition time.

(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.)

FAQ ID: Q-limits
Tags: math