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