Koornwinder polynomials and the
Journal 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
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Nonsymmetric Koornwinder Polynomials and Duality [PDF]
The Annals of Mathematics, 1999 16 pages, published ...
Siddhartha Sahi
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Branching Rules for Koornwinder Polynomials with One Column Diagrams and Matrix Inversions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2020 We present an explicit formula for the transition matrix $\mathcal{C}$ from the type $BC_n$ Koornwinder polynomials $P_{(1^r)}(x|a,b,c,d|q,t)$ with one column diagrams, to the type $BC_n$ monomial symmetric polynomials $m_{(1^{r})}(x)$. The entries of the matrix $\mathcal{C}$ enjoy a set of four terms recursion relations.
Ayumu Hoshino, Jun’ichi Shiraishi
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Specializations of nonsymmetric Macdonald–Koornwinder polynomials [PDF]
Journal of Algebraic Combinatorics, 2017 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
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A difference-integral representation of Koornwinder polynomials [PDF]
, 2004 We construct new families of (q-) difference and (contour) integral operators having nice actions on Koornwinder's multivariate orthogonal polynomials. We further show that the Koornwinder polynomials can be constructed by suitable sequences of these operators applied to the constant polynomial 1, giving the difference-integral representation of the ...
Eric M. Rains
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Quantum spherical functions of type $χ$ as Macdonald-Koornwinder polynomials [PDF]
31 ...
Stein Meereboer
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Representations for parameter derivatives of some Koornwinder polynomials in two variables
Journal of the Egyptian Mathematical Society, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rabi̇a Aktaş
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Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements. [PDF]
Biomed Res Int, 2015 We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics.
Cuccuru G +3 more
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Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials [PDF]
, 2014 We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of the Field and Wimp expansion, Andrews' terminating q-analogue of Watson's 3F2 sum, Singh's quadratic ...
Ayumu Hoshino +2 more
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Some Transformation Formulas Associated with Askey–Wilson Polynomials and Lassalle’s Formulas for Macdonald–Koornwinder Polynomials [PDF]
Moscow Mathematical Journal, 2015 We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of the Field and Wimp expansion, Andrews' terminating q-analogue of Watson's 3F2 sum, Singh's quadratic ...
Ayumu Hoshino +2 more
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