Guide to LaTeX (4th Edition) (Tools and Techniques

12.2. Standard features of A M S-L AT E X 265
which functions in the same way as \frac and the other fraction commands.
\[ \binom{n+1}{k} = \binom{n}{k} n + 1 n n
= +
+ \binom{n}{k-1 \]
k k k − 1
Similarly there are the commands \tbinom and \dbinom analogous to
\tfrac and \dfrac.
User-defined fractions
The amsmath package provides a powerful tool for defining fraction-like
structures:
\genfrac{left brk}{right brk}{thickness}{mathsize}{over}{under}
where left brk and right brk are the parenthesis characters on the left and
right, thickness is the thickness of the horizontal line, and {mathsize} is
a number 0–3 representing the math sizes \displaystyle, \textstyle,
\scriptstyle, and \scriptscriptstyle, respectively. The last two
arguments, over and under, are the texts in the two parts of the fraction,
the same arguments as in \frac and \binom.
If the thickness is left blank, the standard thickness for L AT E X fractions
is used. If mathsize is empty, the font size is determined automatically
by the normal rules in Section 5.5.2.
Rather than repeating \genfrac with the same first four arguments
time and again, one should define new fraction commands with it. For
example, the following definitions are given in amsmath.sty:
\newcommand{\frac}[2]{\genfrac{}{}{}{}{#1}{#2}}
\newcommand{\dfrac}[2]{\genfrac{}{}{}{0}{#1}{#2}}
\newcommand{\tfrac}[2]{\genfrac{}{}{}{1}{#1}{#2}}
\newcommand{\binom}[2]{\genfrac{(}{)}{0pt}{}{#1}{#2}
As a further example, consider the redefinition of the command \frac
\renewcommand{\frac}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
in which the line thickness is now an optional first argument; without this
optional argument, the command behaves as normal. Thus
\[ \binom{n}{m} =
yields n n!
=
\frac[2pt]{n!}{M!(n-m)!} \]
m
M!(n − m)!
Continued fractions
Continued fractions can be made in A M S-L AT E X with the command
\cfrac[pos]{over}{under}
whereby the denominator under may contain further \cfrac commands.