# Constant coefficient Laurent biorthogonal polynomials, Riordan arrays and moment sequences

## TL;DR

This paper investigates constant coefficient Laurent biorthogonal polynomials through Riordan arrays, revealing their properties, related orthogonal polynomials, and explicit formulas for moments and expansions.

## Contribution

It provides new closed-form expressions and detailed analysis of Laurent biorthogonal polynomials and their connections to Riordan arrays and moment sequences.

## Key findings

- Explicit formulas for Laurent biorthogonal polynomials
- Relationships between moments of different polynomial families
- Connections to T-fraction expansions

## Abstract

We study properties of constant coefficient Laurent biorthogonal polynomials using Riordan arrays. We give details of related orthogonal polynomials, and we explore relationships between the moments of these orthogonal polynomials, the moments of the defining Laurent biorthogonal polynomials, and the expansions of $T$-fractions. Closed form expressions are given for the polynomials and their moments.