The TeX syntax
$ … $
is for in-line math mode. It's LaTeX equivalent is
\( … \)
. In in-line math mode limits to operators (integrals, sums, …) are typeset beside them in order not to disturb the line spacing. You can force limits above and below the operators by either using
\limits
directly after an operator command or
\displaystyle
at the beginning of a math expression.
On the other hand
\[ … \]
starts a displayed math environment (for unnumbered equations) where limits are typeset below and above operators by default. To typeset limits beside operators here you can use
\nolimits
as counterpart to the above mentioned
\limits
.
Further reading:
Thorsten