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A chronology of continued square roots and other continued compositions, through the year 2016
An infinite continued composition is an expression of the form
\begin{equation*} \lim_{n\to\infty}t_0\circ t_1 \circ t_2 \circ \cdots \circ
t_n(c)\;, \end{equation*} where the are maps from a set to itself,
the initial value is a point in , and the order of operations proceeds
from right to left.
This document is a bibliography, in chronological order through the year
2016, of selected continued compositions whose primary sources have typically
been obscure. In particular, we include continued square roots:
\begin{equation*} a_0+\sqrt{a_1+\sqrt{a_2+\sqrt{\ldots}}}\;, \end{equation*} as
well as continued powers, continued cotangents, continued logarithms, and
-expansions. However, we do not include continued fractions, continued
exponentials, or forms such as infinite sums and products in which the
are linear functions, because the literature on these forms is extensive.Comment: May be periodically updated; v2: 98 pages, 213 items, topics index,
names inde