View source for Infinite compositions of analytic functions

In [[mathematics]], '''infinite [[Function composition|compositions]] of [[Analytic function|analytic functions]]''' (ICAF) offer alternative formulations of [[Generalized continued fraction|analytic continued fractions]], [[Series (mathematics)|series]], [[Product (mathematics)|products]], and other infinite expansions, and the theory evolving from such compositions may shed light on the [[Limit (mathematics)|convergence/divergence]] of these expansions.

== Description ==

Some functions can actually be expanded directly as infinite compositions.

In addition, it is possible to use ICAF to evaluate solutions of [[Fixed point (mathematics)|fixed point]] equations involving infinite expansions.

[[Complex dynamics]] offers another venue for [[Iterated function system|iteration of systems of functions]] rather than a single function.

For infinite compositions of a single function see [[Iterated function]].

For compositions of a finite number of functions, useful in [[fractal]] theory, see [[Iterated function system]].

== See also ==

* [[Analytic function]]
* [[Function (mathematics)]]
* [[Iterated function]]
* [[Iterated function system]]

== External links ==

* [https://en.wikipedia.org/wiki/Infinite_compositions_of_analytic_functions Infinite compositions of analytic functions] @ Wikipedia

[[Category:Functions]]
[[Category:Mathematics]]