Results 11 to 20 of about 1,056 (198)

Moments of Askey-Wilson polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
New formulas for the $n^{\mathrm{th}}$ moment $\mu_n(a,b,c,d;q)$ of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and ...
Jang Soo Kim, Dennis Stanton
doaj   +5 more sources

Casoratian identities for the Wilson and Askey–Wilson polynomials [PDF]

Journal of Approximation Theory, 2015
31 pages, 2 figures. Comments and references added.
Odake, Satoru, Sasaki, Ryu
exaly   +5 more sources

Multi-indexed Wilson and Askey–Wilson polynomials [PDF]

Journal of Physics A: Mathematical and Theoretical, 2013
As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue ...
Odake, Satoru, Sasaki, Ryu
openaire   +4 more sources

Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials [PDF]

Applicable Analysis, 2011
16 pages. Dedicated to Paul Butzer on the occasion of his 80th birthday. v4: minor correction in (4.14)
Koornwinder, T.H., Bouzeffour, F.
openaire   +6 more sources

Befriending Askey–Wilson polynomials [PDF]

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2014
We recall five families of polynomials constituting a part of the so-called Askey–Wilson scheme. We do this to expose properties of the Askey–Wilson (AW) polynomials that constitute the last, most complicated element of this scheme. In doing so we express AW density as a product of the density that makes q-Hermite polynomials orthogonal times a ...
Paweł J Szabłowski
openaire   +4 more sources

Bootstrapping and Askey–Wilson polynomials

Journal of Mathematical Analysis and Applications, 2015
The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Kim, Jang Soo, Stanton, Dennis
openaire   +5 more sources

Expansions in the Askey–Wilson polynomials

Journal of Mathematical Analysis and Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismail, Mourad E.H., Stanton, Dennis
openaire   +5 more sources

Raising and Lowering Operators for Askey-Wilson Polynomials [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2007
In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties
Siddhartha Sahi
doaj   +4 more sources

Askey–Wilson polynomials, quadratic harnesses and martingales

The Annals of Probability, 2010
We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.
Bryc, Włodek, Wesołowski, Jacek
openaire   +5 more sources

Expansions in Askey–Wilson polynomials via Bailey transform

Journal of Mathematical Analysis and Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia, Zeya, Zeng, Jiang
openaire   +4 more sources