**Tom H. Koornwinder** (born 19 September 1943, in Rotterdam) is a Dutch mathematician at the Korteweg-de Vries Institute for Mathematics who introduced Koornwinder polynomials.

The **Bateman Manuscript Project** was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthur Erdélyi.

In mathematics, the **Askey–Wilson polynomials** are a family of orthogonal polynomials introduced by Askey and Wilson (1985) as q-analogs of the Wilson polynomials. They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme. Askey–Wilson polynomials are the special case of Macdonald polynomials for the non-reduced affine root system of type, and their 4 parameters a, b, c, d correspond to the 4 orbits of roots of this root system.

In mathematics, **Charlier polynomials** are a family of orthogonal polynomials introduced by Carl Charlier. They are given in terms of the generalized hypergeometric function by

In mathematics, **Macdonald-Koornwinder polynomials** (also called **Koornwinder polynomials**) are a family of orthogonal polynomials in several variables, introduced by Koornwinder (1992) and I. G. Macdonald (1987, important special cases), that generalize the Askey–Wilson polynomials. They are the Macdonald polynomials attached to the non-reduced affine root system of type (*C*^{∨}_{n}, *C*_{n}), and in particular satisfy (van Diejen 1996, Sahi 1999) analogues of Macdonald's conjectures (Macdonald 2003, Chapter 5.3). In addition Jan Felipe van Diejen showed that the Macdonald polynomials associated to any classical root system can be expressed as limits or special cases of Macdonald-Koornwinder polynomials and found complete sets of concrete commuting difference operators diagonalized by them (van Diejen 1995). Furthermore, there is a large class of interesting families of multivariable orthogonal polynomials associated with classical root systems which are degenerate cases of the Macdonald-Koornwinder polynomials (van Diejen 1999). The Macdonald-Koornwinder polynomials have also been studied with the aid of affine Hecke algebras (Noumi 1995, Sahi 1999, Macdonald 2003).

In mathematics, **Stieltjes–Wigert polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function

In mathematics, the **continuous dual q-Hahn polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **dual q-Hahn polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **big q-Jacobi polynomials**

In mathematics, the **big q-Laguerre polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **affine q-Krawtchouk polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Carlitz and Hodges. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **dual q-Krawtchouk polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **continuous big q-Hermite polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **little q-Laguerre polynomials**

In mathematics, the ** q-Meixner–Pollaczek polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the ** q-Meixner polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the **quantum q-Krawtchouk polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

In mathematics, the ** q-Krawtchouk polynomials** are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14). give a detailed list of their properties.

**Carl Samuel Herz** was an American-Canadian mathematician, specializing in harmonic analysis. His name is attached to the Herz–Schur multiplier. He held professorships at Cornell University and McGill University, where he was Peter Redpath Professor of Mathematics at the time of his death.

**Arnoldus Bernardus Jacobus Kuijlaars** is a Dutch mathematician, specializing in approximation theory.

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