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- Koornwinder_polynomials abstract "In mathematics, Koornwinder polynomials (also called Macdonald–Koornwinder polynomials) are a family of orthogonal polynomials in several variables, introduced by Koornwinder (1992), that generalize the Askey–Wilson polynomials. They are the Macdonald polynomials attached to the non-reduced affine root system of type (C∨n, Cn), and in particular satisfy (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 Koornwinder polynomials and found complete sets of concrete commuting difference operators diagonalized by them (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 Koornwinder-Macdonald polynomials (Diejen 1999). The Koornwinder-Macdonald polynomials have also been studied with the aid of affine Hecke algebras (Noumi 1995, Sahi 1999, Macdonald 2003).The Koornwinder polynomial in n variables associated to the partition λ is the unique Laurent polynomial invariant under permutation and inversion of variables, with leading monomial xλ, and orthogonal with respect to the densityon the unit torus,where the parameters satisfy the constraintsand (x;q)∞ denotes the infinite q-Pochhammer symbol.Here leading monomial xλ means that μ≤λ for all terms xμ with nonzero coefficient, where μ≤λ if and only if μ1≤λ1, μ1+μ2≤λ1+λ2, …, μ1+…+μn≤λ1+…+λn.Under further constraints that q and t are real and that a, b, c, d are real or, if complex, occur in conjugate pairs, the given density is positive.For some lecture notes on Koornwinder polynomials from a Hecke algebra perspective see for example (Stokman 2004).".
- Koornwinder_polynomials wikiPageID "19599247".
- Koornwinder_polynomials wikiPageRevisionID "562206195".
- Koornwinder_polynomials b "n".
- Koornwinder_polynomials hasPhotoCollection Koornwinder_polynomials.
- Koornwinder_polynomials p "∨".
- Koornwinder_polynomials subject Category:Orthogonal_polynomials.
- Koornwinder_polynomials type Abstraction100002137.
- Koornwinder_polynomials type Function113783816.
- Koornwinder_polynomials type MathematicalRelation113783581.
- Koornwinder_polynomials type OrthogonalPolynomials.
- Koornwinder_polynomials type Polynomial105861855.
- Koornwinder_polynomials type Relation100031921.
- Koornwinder_polynomials comment "In mathematics, Koornwinder polynomials (also called Macdonald–Koornwinder polynomials) are a family of orthogonal polynomials in several variables, introduced by Koornwinder (1992), that generalize the Askey–Wilson polynomials. They are the Macdonald polynomials attached to the non-reduced affine root system of type (C∨n, Cn), and in particular satisfy (Diejen 1996, Sahi 1999) analogues of Macdonald's conjectures (Macdonald 2003, Chapter 5.3).".
- Koornwinder_polynomials label "Koornwinder polynomials".
- Koornwinder_polynomials sameAs m.04mytxx.
- Koornwinder_polynomials sameAs Q6430769.
- Koornwinder_polynomials sameAs Q6430769.
- Koornwinder_polynomials sameAs Koornwinder_polynomials.
- Koornwinder_polynomials wasDerivedFrom Koornwinder_polynomials?oldid=562206195.
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