A short survey of duality in special functions

TL;DR

This paper provides a tutorial overview of duality properties in special functions, focusing on orthogonal polynomials within the ($q$-)Askey scheme, highlighting their mathematical relationships and symmetries.

Contribution

It offers a comprehensive survey of duality concepts in special functions, consolidating existing knowledge and presenting it in an accessible tutorial format.

Findings

Clarifies duality properties of orthogonal polynomials

Summarizes key duality relations in the ($q$-)Askey scheme

Serves as an educational resource for researchers and students

Abstract

This is a tutorial on duality properties of special functions, mainly of orthogonal polynomials in the ($q$-)Askey scheme. It is based on the first part of the 2017 R.P. Agarwal Memorial Lecture delivered by the author.