On a closed form of rational generating functions for polynomials

TL;DR

This paper derives a closed-form expression for rational generating functions that produce various polynomial families, enabling the determination of their recursive formulas.

Contribution

It introduces a closed-form solution for rational generating functions that generate polynomial families, advancing understanding of their recursive structures.

Findings

Closed-form expressions for rational generating functions obtained.

Recursive formulas for polynomial families derived.

Framework applicable to generalized polynomials.

Abstract

Our goal in this work is to found a closed form for rational generat- ing functions, these generate a various families of polynomials and generalized polynomials, in order to get the general recursive formula satisfied by these polynomials.