Results 71 to 80 of about 2,532 (147)

A Probablistic Origin for a New Class of Bivariate Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2008
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
doaj   +1 more source

Wiman-Valiron theory for a polynomial series based on the Askey-Wilson operator [PDF]

, 2020
Kam Hang Cheng, Yik‐Man Chiang
openalex   +1 more source

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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Nonsymmetric Askey–Wilson polynomials and Q-polynomial distance-regular graphs

Journal of Combinatorial Theory, Series A, 2017
In his famous theorem (1982), Douglas Leonard characterized the $q$-Racah polynomials and their relatives in the Askey scheme from the duality property of $Q$-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the $q$-Racah polynomials in the above situation.
openaire   +3 more sources

On First type characterizations of Askey-Wilson polynomials

, 2023
In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.
Mbouna, D., Suzuki, A.
openaire   +2 more sources

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.
core   +1 more source

A "missing" family of classical orthogonal polynomials

, 2011
We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type.
Alexei Zhedanov, Askey R A, Atia M J, Bannai E, Chihara T, Dunkl C F, Geronimus Ya L, Ince E L, Ismail M E H, Ito T, Koekoek R Swarttouw R, Luc Vinet, Spiridonov V, Spiridonov V, Szegő G, Zhedanov A S   +15 more
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Askey-Wilson polynomials: an affine Hecke algebraic approach

, 2000
We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetric Askey-Wilson polynomials with respect to a complex measure.
Noumi, M., Stokman, J.V.
openaire   +3 more sources

8 Lectures on quantum groups and q-special functions [PDF]

, 1996
Lecture notes for an eight hour course on quantum groups and $q$-special functions at the fourth Summer School in Differential Equations and Related Areas, Universidad Nacional de Colombia and Universidad de los Andes, Bogot\'a, Colombia, July 22 ...
Koelink, Erik
core   +3 more sources

On the families of polynomials forming a part of the Askey–Wilson scheme and their probabilistic applications [PDF]

, 2022
Paweł J. Szabłowski
openalex   +1 more source