# Eulerian-Dowling Polynomials as Moments, Using Riordan Arrays

## TL;DR

This paper demonstrates that Eulerian-Dowling polynomials and related polynomials are moments of orthogonal polynomial families, providing continued fractions and Hankel transforms to analyze their properties.

## Contribution

It establishes the connection between Eulerian-Dowling polynomials and orthogonal polynomials using Riordan arrays, introducing new moment representations and generating functions.

## Key findings

- Eulerian-Dowling polynomials are moments for orthogonal polynomials.
- Continued fraction generating functions are derived for these polynomials.
- Hankel transforms of the polynomials are computed.

## Abstract

Using the theory of exponential Riordan arrays, we show that the Eulerian-Dowling polynomials are moments for a paramaterized family of orthogonal polynomials. In addition, we show that the related Dowling and the Tanny-Dowling polynomials are also moments for appropriate families of orthogonal polynomials. We provide continued fraction generating functions and Hankel transforms for these polynomials.