Results 201 to 210 of about 3,786,908 (243)

The daily auditory environments of people with tinnitus. [PDF]

open access: yesSci Rep
Skoe E   +10 more
europepmc   +1 more source

Expansions in the Askey–Wilson polynomials

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

On a conjecture involving Askey–Wilson polynomials

Integral Transforms and Special Functions
The following relation holds: $$\begin{align*} & \left(\left(\frac{q^{1/2} +q^{-1/2}}{2}\right) ^2-1\right)^2\left(x^2 -\left(\frac{q^{1/2} +q^{-1/2}}{2}\right) ^2\right)\notag\\ & \quad (1-x^2)\, \mathcal{D}_q^2\, P_n(x;1,q^{1/2}, 0, 0\,|\, q ...
K Castillo, D Mbouna
exaly   +2 more sources

Asymptotics of the Wilson polynomials

Analysis and Applications, 2019
In this paper, we study the asymptotic behavior of the Wilson polynomials [Formula: see text] as their degree tends to infinity. These polynomials lie on the top level of the Askey scheme of hypergeometric orthogonal polynomials.
Yutian Li, Xiang-Sheng Wang, R. Wong
semanticscholar   +3 more sources

Bootstrapping and Askey–Wilson polynomials

open access: yesJournal 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.
Jang Soo Kim, Dennis Stanton
exaly   +4 more sources

New recurrence relations for Wilson polynomials via a system of Jacobi type orthogonal functions

Journal of Mathematical Analysis and Applications, 2021
In this paper, we will find an orthogonal basis in term of explicit Jacobi polynomials, of the corresponding weighted L 2 -space on the whole of the real numbers, which is mapped onto another orthogonal basis involving Wilson polynomials by the Jacobi ...
N. Abdallah, F. Chouchene
semanticscholar   +1 more source

On the Askey-Wilson polynomials

Constructive Approximation, 1992
Classical orthogonal polynomials of a discrete variable on non-uniform lattices were introduced by \textit{R. Askey} and \textit{J. A. Wilson} [SIAM J. Math. Anal. 10, 1008-1016 (1979; Zbl 0437.33014)], and \textit{J. A. Wilson} [ibid. 11, 690-701 (1980; Zbl 0454.33007)] and their main properties were established on the basis of the theory of ...
N M Atakishiyev, S K Suslov
exaly   +3 more sources

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