Results 11 to 20 of about 2,394 (105)
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
Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials [PDF]
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 2009 Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which ...
Alberto Grünbaum +35 more
core +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.Comment: Published ...
Bryc, Włodek, Wesołowski, Jacek
core +3 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
On Another Characterization of Askey-Wilson Polynomials
Results in Mathematics, 2022 In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} ϕ(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $ϕ$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson ...
Mbouna, D., Suzuki, A.
openaire +4 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
openaire +4 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
Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials [PDF]
Journal of Mathematical Physics, 2004 We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters.
Askey R. +3 more
core +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
The factorization method for the Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 1999 A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.
openaire +5 more sources