Results 41 to 50 of about 2,943 (105)

Nevanlinna Theory of the Wilson Divided-difference Operator

, 2017
Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference equation in terms of ...
Cheng, Kam Hang, Chiang, Yik-Man
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Bivariate Bannai-Ito polynomials

, 2018
A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These
Lemay, Jean-Michel, Vinet, Luc
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Askey-Wilson Type Functions, With Bound States

, 2003
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful ...
A. Kasman, A.S. Zhedanov, B. Bakalov, B. Bakalov, D. Mumford, E. Koelink, F.A. Grünbaum, F.A. Grünbaum, F.A. Grünbaum, F.A. Grünbaum, F.W. Nijhoff, G. Andrews, G. Segal, G. Wilson, G. Wilson, H.L. Krall, I. Cherednik, J. Koekoek, J.J. Duistermaat, L. Haine, L. Haine, L. Haine, L.L. Littlejohn, Luc Haine, M. Rahman, M. Rahman, M. Toda, M.E.H. Ismail, P. Iliev, P. Iliev, Plamen Iliev, S. Bochner, S.K. Suslov, S.K. Suslov, T.H. Koornwinder, V.P. Spiridonov, W.N. Everitt   +36 more
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Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy [PDF]

, 2012
A $\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\mathbb{D}$.
Witte, N. S.
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Wilson function transforms related to Racah coefficients

, 2005
The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series.
A.N. Kirillov, D.P. Gupta, E. Buffenoir, E. Koelink, E.G. Kalnins, G. Gasper, G. Racah, G.A. Kerimov, G.A. Kerimov, H. Rosengren, H.T. Koelink, H.T. Koelink, H.T. Koelink, H.T. Koelink, I.M. Burban, J.A. Wilson, J.P. Elliott, J.V. Stokman, J.V. Stokman, K. Schmüdgen, L.C. Biedenharn, L.C. Biedenharn, L.L. Vaksman, M. Noumi, N.J. Vilenkin, R. Askey, R. Askey, R. Koekoek, S. Lievens, T.H. Koornwinder, T.H. Koornwinder, T.H. Koornwinder, V. Bargmann, W. Groenevelt, W. Groenevelt, W. Groenevelt, Wolter Groenevelt, Y.F. Smirnov   +37 more
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Orthogonal Polynomials in Mathematical Physics

, 2017
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory.
Chan, Chuan-Tsung, Mironov, A., Morozov, A., Sleptsov, A.   +3 more
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A Lie algebra related to the universal Askey-Wilson algebra

, 2015
Let $\mathbb{F}$ denote an algebraically closed field. Denote the three-element set by $\mathcal{X}=\{A,B,C\}$, and let $\mathbb{F}\left$ denote the free unital associative $\mathbb{F}$-algebra on $\mathcal{X}$. Fix a nonzero $q\in\mathbb{F}$ such that $q^4\neq 1$. The universal Askey-Wilson algebra $ $ is the quotient space $\mathbb{F}\left/\mathbb{I}
openaire   +3 more sources

A note on the $O_q(\hat{sl_2})$ algebra

, 2010
An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian algebra generating $O_q(\hat{sl_2})$ currents and the standard generators of the $q-$Onsager algebra is proposed.
Baseilhac, P., Belliard, S.
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations

, 1996
The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to generalisations of the ...
Koelink, H. T., Van der Jeugt, J.
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A generalization of the Askey-Wilson relations using a projective geometry

In this paper, we present a generalization of the Askey-Wilson relations that involves a projective geometry. A projective geometry is defined as follows. Let $h>k\geq 1$ denote integers. Let $\mathbb{F}_{q}$ denote a finite field with $q$ elements. Let $\mathcal{V}$ denote an $(h+k)$-dimensional vector space over $\mathbb{F}_{q}$.
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