Additions to the formula lists in "Hypergeometric orthogonal polynomials and their $q$-analogues" by Koekoek, Lesky and Swarttouw

TL;DR

This paper compiles additions to formulas for ($q$-)hypergeometric orthogonal polynomials within the $q$-Askey scheme that were overlooked in Koekoek–Lesky–Swarttouw, organized to mirror Chapters 9 and 14 of the reference text. It covers orthogonality measures, kernel polynomials, symmetry, generating functions, special values, and various transformations for a wide spectrum of families (e.g., Wilson, Racah, Jacobi, Hahn, Meixner–Pollaczek, Krawtchouk, Laguerre, Laguerre-type, Bessel/Romanovski, and their $q$-analogues), including numerous q-difference equations and limit relations. The notes emphasize measure-uniqueness criteria, three-term recurrences, bilinear and Appell-type generating functions, and explicit connections between classical and $q$-versions through quadratic and limit transformations. The compilation serves as a practical companion for researchers needing quick lookups, proofs, or corrections to identities in the Askey scheme, and it also situates many results in historical and notational contexts. Overall, it enhances the usability of the $q$-Askey framework by collecting non-primary yet frequently-used identities with concise references and sketches of proofs.

Abstract

This paper gives a rather arbitrary choice of formulas for ($q$-)hypergeometric orthogonal polynomials which the author missed while consulting Chapters 9 and 14 in the book "Hypergeometric orthogonal polynomials and their $q$-analogues" by Koekoek, Lesky and Swarttouw. The systematics of these chapters will be followed here, in particular for the numbering of subsections and of references.