# On the restricted Chebyshev-Boubaker polynomials

## TL;DR

This paper introduces and analyzes a new family of orthogonal polynomials called restricted Chebyshev-Boubaker polynomials, using Riordan arrays to characterize their properties, recurrences, and moment sequences.

## Contribution

It characterizes the polynomials via three-term recurrences, provides integral representations for moments, and explores their Hankel transforms and relations to Chebyshev polynomials.

## Key findings

- Hankel transforms of moments have a simple form
- Row sums of the moment matrix relate to Chebyshev polynomials
- Row sums are moments of another orthogonal polynomial family

## Abstract

Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev-Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they satisfy, and we study certain central sequences defined by their coefficient arrays. We give an integral representation for their moments, and we show that the Hankel transforms of these moments have a simple form. We show that the (sequence) Hankel transform of the row sums of the corresponding moment matrix is defined by a family of polynomials closely related to the Chebyshev polynomials of the second kind, and that these row sums are in fact the moments of another family of orthogonal polynomials.