I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions with two parameters VII. Zonal polynomials

Symmetric functions and Hall polynomials

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed Orthogonal polynomials on the unit circle are not discussed

Orthogonal Polynomials

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs

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The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

The quantum group SU(2)q is discussed by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum Such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose, is developed

https://iopscience.iop.org/article/10.1088/0305-4470/22/21/020/pdf

On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q

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.

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

Dual equations and classical orthogonal polynomials

Special Functions: The Selberg Integral and Its Applications

Positivity of the Cotes Numbers for Some Ultraspherical Abscissas

A conjecture of I. G. Macdonald [SIAM J. Math. Anal. 13 (1982), pp. 988–1007] about the constant term in a Laurent polynomial expansion associated with the affine root system of $BC_1 $ is extended and then proved by evaluation of an integral that extends a beta function integral.

A q-Beta Integral Associated with $BC_1 $

Some old quadrature schemes are shown to be positive.

Richard Askey

Papers

Dual equations and classical orthogonal polynomials

Special Functions: The Selberg Integral and Its Applications

Positivity of the Cotes Numbers for Some Ultraspherical Abscissas

A q-Beta Integral Associated with $BC_1 $

Positivity of the cotes numbers for some Jacobi abscissas