Composition of ordinary generating functions

TL;DR

This paper introduces a new class of functions for composing ordinary generating functions, presents main theorems, and demonstrates the composition's applicability to various functions and integer sequences.

Contribution

It proposes a novel class of functions enabling composition of ordinary generating functions, expanding theoretical understanding and practical applications.

Findings

Composition holds for polynomials, trigonometric, hyperbolic, exponential, and logarithmic functions.

Compositae are derived for various function classes.

Many integer sequences can be represented through this composition method.

Abstract

A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written for polynomials, trigonometric and hyperbolic functions, exponential and log functions. It is shown that the composition holds true for many integer sequences.