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TeX’s rules for typesetting a formula depend on the context. For
example, inside a displayed equation, the input \sum_{0\leq
i<n}k^m=\frac{n^{m+1}}{m+1}+\mbox{lower order terms}
will give
output with the summation index centered below the summation symbol.
But if that input is inline then the summation index is off to the right
rather than below, so it won’t push the lines apart. Similarly, in a
displayed context, the symbols in the numerator and denominator will be
larger than for an inline context, and in display math subscripts and
superscripts are further apart then they are in inline math.
TeX uses four math styles.
\begin{equation} ... \end{equation}
.
TeX determines a default math style but you can override it with a
declaration of \displaystyle
, or \textstyle
, or
\scriptstyle
, or \scriptscriptstyle
.
In this example, the ‘Arithmetic’ line’s fraction will look scrunched.
\begin{tabular}{r|cc} \textsc{Name} &\textsc{Series} &\textsc{Sum} \\ \hline Arithmetic &$a+(a+b)+(a+2b)+\cdots+(a+(n-1)b)$ &$na+(n-1)n\cdot\frac{b}{2}$ \\ Geometric &$a+ab+ab^2+\cdots+ab^{n-1}$ &$\displaystyle a\cdot\frac{1-b^n}{1-b}$ \\ \end{tabular}
But because of the \displaystyle
declaration,
the ‘Geometric’ line’s fraction will be easy to read, with
characters the same size as in the rest of the line.
Another example is that, compared to the same input without the declaration, the result of
we get $\pi=2\cdot{\displaystyle\int_{x=0}^1 \sqrt{1-x^2}\,dx}$
will have an integral sign that is much taller. Note that here the
\displaystyle
applies to only part of the formula, and it is
delimited by being inside curly braces, as ‘{\displaystyle ...}’.
The last example is a continued fraction.
\begin{equation} a_0+\frac{1}{ \displaystyle a_1+\frac{\mathstrut 1}{ \displaystyle a_2+\frac{\mathstrut 1}{ \displaystyle a_3}}} \end{equation}
Without the \displaystyle
declarations, the denominators would be
set in script style and scriptscript style. (The \mathstrut
improves the height of the denominators; see \mathstrut
.)