Shifted Hankel determinants of Catalan numbers and related results

TL;DR

This paper explores the relationship between Catalan numbers and Hankel determinants through orthogonal polynomials, extending the analysis to more general sequences, providing insights into their mathematical structure.

Contribution

It offers a concise overview of the connection between Catalan numbers and Hankel determinants and generalizes this relationship to broader classes of sequences.

Findings

Catalan numbers are closely linked to Hankel determinants via orthogonal polynomials.

The relationship between these mathematical objects extends to more general sequences.

The paper provides an expository overview of these connections.

Abstract

In this (partly expository) paper we give a short overview about the close relationship between the sequence of Catalan numbers and Hankel determinants from the point of view of orthogonal polynomials and show that an analogous situation exists for more general sequences.