Infinite compositions of analytic functions

In mathematics, infinite compositions of analytic functions (ICAF) offer alternative formulations of analytic continued fractions, series, products, and other infinite expansions, and the theory evolving from such compositions may shed light on the 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 equations involving infinite expansions.

Complex dynamics offers another venue for 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.