Operators; Sums, Integrals, etc.

Each of the operation symbols in table [*] can occur with limits. They are specified as sub- and superscripts to the operator, and LATEX will position them appropriately. In an in-text formula they will appear in more-or-less the usual scripting positions; but in a displayed formula they will be set below and above the symbol (which will also be a little larger). The following should give you an idea of how to use them:

\begin{mathegs}
\verb@$\sum_{i=1}^{N} a_i$@ & $\sum_{i=1}^{N} a_i$\\
\verb@$\in...
... x_i$@ & $\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i$
\end{mathegs}

We'll have more to say about the use of \, in section [*]. Let's have a look at each of those expressions when displayed:

$\displaystyle \sum_{{i=1}}^{{N}}$ai    ,    $\displaystyle \int_{a}^{b}$f    ,    $\displaystyle \oint_{{\cal C}}^{}$f (x) dx    ,    $\displaystyle \prod_{{\alpha \in A}}^{}$Xα    ,    $\displaystyle \lim_{{N\rightarrow\infty}}^{}$$\displaystyle \sum_{{i=1}}^{{N}}$f (xi)Δxi