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A short survey of duality in special functions

Tom H. Koornwinder

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.

A short survey of duality in special functions

Abstract

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

Paper Structure

This paper contains 12 sections, 36 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Note
  3. The notion of duality in special functions
  4. The Askey scheme
  5. Classical OPs
  6. Discrete analogues of classical OPs
  7. Continuous versions of Hahn and Meixner polynomials
  8. Insertion of a quadratic argument
  9. The $q$-Askey scheme
  10. Duality for non-polynomial special functions
  11. Some further cases of duality
  12. Acknowledgement

Figures (1)

  • Figure 1: The Askey scheme