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

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.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Analytic Number Theory Research
