fractions
How does one typeset the following continued fraction as shown below?
Source: Notes on continued fractions and recurrence sequences by Alfred van der Poorten.
Note: Alf van der Poorten's style is similar to Euler's (in E071).
Source: The Euler Archive, Index Number E71.
A couple of versions, you probably need to fiddle with the spacing to get exactly what you need but:
\documentclass{article}
\def\cFrac#1#2{%
\begin{array}{@{}c@{}}\multicolumn{1}{c|}{#1}\\%
\hline\multicolumn{1}{|c}{#2}\end{array}}
\def\cFracB#1#2{%
\vcenter{\hbox{\strut$#1$\,\vrule}\hrule\hbox{\strut\vrule\,$#2$}}}
\begin{document}
$ A + \cFrac{B}{C} + \cFrac{D}{E}$.
$ A + \cFracB{B}{C} + \cFracB{D}{E}$.
\end{document}
Just use a bmatrix environment in the denominator:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
b\cdot[0;a_1,a_2,a_3,\cdots]=\cfrac{b}{a_1+\cfrac{1}{a_2+\cfrac{1}{a_3+\cdots}}}=
\cfrac{1}{\cfrac{1}{b} \begin{bmatrix} a_1+\cfrac{1}{a_2+\cfrac{1}{a_3+\cdots}} \end{bmatrix}}
\]
\end{document}
Best Answer
This variant saves a vertical space. Because of the shortened line, there is many free space above the continued fractions that is used in this example. Also it keeps the math axis for the summations.