Hankel determinants of some polynomial sequences

TL;DR

This paper provides new, simplified proofs for existing Hankel determinant evaluations and extends these results to sums of moments of symmetric orthogonal polynomials, enhancing understanding of polynomial sequence properties.

Contribution

It introduces simplified proof techniques for known Hankel determinant evaluations and generalizes results to symmetric orthogonal polynomial moments.

Findings

Simplified proofs for Hankel determinant evaluations.

Extension of results to sums of moments of symmetric orthogonal polynomials.

New identities relating polynomial sequences and determinants.

Abstract

We give simple new proofs of some Hankel determinant evaluations by Omer Egecioglu and Aleksandar Cvetkovic, Predrag Rajkovic and Milos Ivkovic and prove analogous results for sums of moments of symmetric orthogonal polynomials.