Some observations about super Catalan numbers, corresponding orthogonal polynomials, and their q-analogues

TL;DR

This paper surveys polynomials related to super Catalan numbers, explores their q-analogues, and discusses their orthogonal properties, providing insights into their mathematical structure and generalizations.

Contribution

It introduces two different q-analogues of polynomials associated with super Catalan numbers and examines their orthogonal properties.

Findings

Identification of polynomials with moments as super Catalan numbers

Development of two q-analogues of these polynomials

Insights into their orthogonal polynomial structure

Abstract

In this note we give a survey about polynomials whose moments are multiples of super Catalan numbers and explore two different kinds of q-analogues.