Convergence of Infinite Composition of Entire Functions
Shota Kojima
TL;DR
This paper investigates conditions under which infinite compositions of entire functions result in an entire function, including an analysis of Poincaré functions as key examples.
Contribution
It establishes criteria for the convergence of infinite compositions of entire functions and explores the properties of Poincaré functions within this context.
Findings
Derived conditions for the convergence of infinite compositions
Characterized when such compositions are entire functions
Analyzed properties of Poincaré functions as examples
Abstract
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions becomes an entire function. Moreover, as an example of such functions, we study a function called Poincare function.
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Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals · Analytic and geometric function theory