Sum-class symbol

Sum-class symbols are symbols whose sub- and superscripts appear directly below and above the symbol rather than beside it. For example, the following example illustrates that \sum is one of these elite symbols whereas \Sigma is not. The terminology from AMS-LaTeX documentation.

\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}

$\sum _{i=1}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}$

\Sigma_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}

$\Sigma _{i=1}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}$

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.

\prod_{i=1}^n x = x^n

$\prod _{i=1}^{n}x=x^{n}$