Results 31 to 40 of about 2,254 (120)

Specializations of nonsymmetric Macdonald-Koornwinder polynomials [PDF]

open access: greenJournal of Algebraic Combinatorics, 2013
This work records the details of the Ram-Yip formula for nonsymmetric Macdonald-Koornwinder polynomials for the double affine Hecke algebras of not-necessarily-reduced affine root systems. It is shown that the t=0 equal-parameter specialization of nonsymmetric Macdonald polynomials admits an explicit combinatorial formula in terms of quantum alcove ...
Daniel L. Orr, Mark Shimozono
openalex   +5 more sources

Koornwinder polynomials and the XXZ spin chain [PDF]

open access: greenJournal of Approximation Theory, 2014
30 pages; corrected some minor mistakes immediately before and after Def. 3.6. appears in Journal of Approximation Theory (2014)
Jasper V. Stokman, Bart Vlaar
openalex   +8 more sources

On a Differential Equation for Koornwinder's Generalized Laguerre Polynomials [PDF]

open access: yesProceedings of the American Mathematical Society, 1991
Koornwinder’s generalized Laguerre polynomials { L n α , N ( x ) } n = 0 ∞ \left \{ {L_n^{\alpha ,N}
J. Koekoek, Roelof Koekoek
openaire   +2 more sources

A review of multivariate orthogonal polynomials

open access: yesJournal of the Egyptian Mathematical Society, 2017
This paper contains a brief review of orthogonal polynomials in two and several variables. It supplements the Koornwinder survey [40]. Several recently discovered systems of orthogonal polynomials have been treated in this work.
Mourad E.H. Ismail, Ruiming Zhang
doaj   +1 more source

Representations for the parameter derivatives of some Koornwinder polynomials

open access: green, 2015
In 1975, Koornwinder gave a method to construct orthogonal polynomials in two variables using the classical Jacobi polynomials. In [5], the authors introduced some new examples of Koornwinder polynomials obtained from the Koornwinder construction (see also [10]).
Rabıa Aktaş
openalex   +4 more sources

The Fractional Orthogonal Derivative

open access: yesMathematics, 2015
This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n.
Enno Diekema
doaj   +1 more source

Quadratic transformations for orthogonal polynomials in one and two variables [PDF]

open access: yes, 2018
We discuss quadratic transformations for orthogonal polynomials in one and two variables. In the one-variable case we list many (or all) quadratic transformations between families in the Askey scheme or $q$-Askey scheme. In the two-variable case we focus,
Koornwinder, Tom H.
core   +2 more sources

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