Sum-class symbols, or accumulation symbols, are symbols whose sub- and superscripts appear directly below and above the symbol rather than beside it.
Table of sum-class symbols
TeX is smart enough to only show
\sum in its expanded form in the displaymath environment. In the regular math environment,
\sum does the right thing and revert to non-sum-class behavior, thus conserving vertical space.
Another common sum-class symbol is
\prod. As in
\sum we can use the directive
\nolimits in order to show the limits on top-down or on the right.