We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. 
In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.

/pdf/the-askey-scheme-of-hypergeometric-orthogonal-polynomials-46afheftah.pdf

The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Mathematica--A System for Doing Mathematics by Computer.

Zeros of orthogonal polynomials

When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Ei…

Bose-Einstein condensation

Discussion of the most important formulae and construction of plots for some functions of mathematical physics relevant to quantum mechanics. These functions are Hermite polynomials, Legendre polynomials and Legendre functions, spherical harmonics, Bessel functions and spherical Bessel functions and Laguerre polynomials. Directly related to some of these and also discussed are the eigenfunctions of the one-dimensional harmonic oscillator and the radial eigenfunctions of the harmonics oscillator in three dimensions and of the hydrogen atom.

Renato Alvarez-Nodarse

Papers

On characterizations of classical polynomials

On the q -polynomials: a distributed study

On the “Favard theorem” and its extensions

Asymptotic properties of generalized Laguerre orthogonal polynomials

q -Classical polynomials and the q -Askey and Nikiforov-Uvarov tableaus