Results 11 to 20 of about 2,393 (108)
A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also đq-Appell where đq is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
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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 GrĂŒnbaum +35 more
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Befriending AskeyâWilson polynomials [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2014 We recall five families of polynomials constituting a part of the so-called AskeyâWilson scheme. We do this to expose properties of the AskeyâWilson (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 ...
PaweĆ J SzabĆowski
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Expansions in the AskeyâWilson polynomials
Journal of Mathematical Analysis and Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismail, Mourad E.H., Stanton, Dennis
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Multi-indexed Wilson and AskeyâWilson 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
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Bootstrapping and AskeyâWilson 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
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Casoratian identities for the Wilson and AskeyâWilson polynomials [PDF]
Journal of Approximation Theory, 2015 31 pages, 2 figures. Comments and references added.
Odake, Satoru, Sasaki, Ryu
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Expansions in AskeyâWilson 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
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Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Gasper followed the fractional calculus proof of an ErdĂ©lyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulationâbased proof of the ErdĂ©lyi integral, due to âJoshi and Vyasâ. Motivated from this alternative way of
Yashoverdhan Vyas +5 more
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The Associated Askey-Wilson Polynomials [PDF]
Transactions of the American Mathematical Society, 1991 The most general system of basic hypergeometric orthogonal polynomials are the Askey-Wilson polynomials, which are given as a basic hypergeometric series \(_ 4\Phi_ 3\). Like all orthogonal polynomials they satisfy a three-term recurrence relation \[ 2xp_ n(x)=A_ np_{n+1}(x)+B_ np_ n(x)+C_ np_{n-1}(x). \] The recurrence coefficients \(A_ n\), \(B_ n\),
Ismail, Mourad E. H., Rahman, Mizan
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