# Riordan arrays, Chebyshev polynomials, Fibonacci bases

## TL;DR

This paper explores the connections between Chebyshev polynomials, Riordan matrices, and Fibonacci bases, demonstrating how these mathematical structures can be used to construct bases for formal power series and polynomials.

## Contribution

It introduces the concept of Fibonacci bases constructed from Riordan matrices associated with Chebyshev polynomials, highlighting their properties and applications.

## Key findings

- Riordan matrices relate to Chebyshev polynomials and Fibonacci sequences.
- Fibonacci bases can be built using columns and rows of Riordan matrices.
- Properties of these bases facilitate their use in polynomial and power series spaces.

## Abstract

Chebyshev polynomials and their modifications are attributes of various fields of mathematics. In particular, they are generating functions of the rows elements of certain Riordan matrices. In paper, we give a selection of some characteristic situations in which such matrices are involved. Using the columns and rows of these matrices, we will build the bases of the space of formal power series and the space of polynomials, the properties of which allow us to call them "Fibonacci bases".