Results 21 to 30 of about 45,205 (253)
A Characterization of Askey-Wilson polynomials
Proceedings of the American Mathematical Society, 2017 We show that the only monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$ that satisfy $$ (x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos ,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $ (x)$ is a polynomial of degree at most $4$ and $\mathcal{D}_{q}$ is the Askey-Wilson operator, are Askey-Wilson polynomials and their ...
Maurice Kenfack Nangho, Kerstin Jordaan
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Multiple Wilson and Jacobi–Piñeiro polynomials
Journal of Approximation Theory, 2005 22 pages, 2 ...
Bernhard Beckermann +2 more
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On Some Limit Cases of Askey–Wilson Polynomials
Journal of Approximation Theory, 1998 AbstractWe show that limit transitions from Askey–Wilson polynomials toq-Racah, little and bigq-Jacobi polynomials can be made rigorous on the level of their orthogonality measures in a suitable weak sense. This allows us to derive the orthogonality relations and norm evaluations for theq-Racah polynomials, little and bigq-Jacobi polynomials by taking ...
Jasper V. Stokman, Tom H. Koornwinder
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Casoratian identities for the Wilson and Askey–Wilson polynomials [PDF]
Journal of Approximation Theory, 2015 31 pages, 2 figures. Comments and references added.
Ryu Sasaki, Satoru Odake
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Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials [PDF]
Letters in Mathematical Physics, 2021 AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles.
Tamara Grava +3 more
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Remarks on Askey–Wilson polynomials and Meixner polynomials of the second kind [PDF]
The Ramanujan Journal, 2021 The purpose of this note is twofold: firstly to characterize all the sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ such that $$ \frac{\triangle}{{\bf \triangle} x(s-1/2)}P_{n+1}(x(s-1/2))=c_n(\triangle +2\,\mathrm{I})P_n(x(s-1/2)), $$ where $\mathrm{I}$ is the identity operator, $x$ defines a class of lattices with, generally, nonuniform step ...
K. Castillo, D. Mbouna, J. Petronilho
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Two Strategies for Researching the Endangered Yangtze Finless Porpoises Suggest Data-Poor Areas Are Worthy of Greater Conservation Efforts. [PDF]
Ecol EvolTwo strategies were used to assess the abundance and distribution of Yangtze finless porpoises in the Jingjiang section of the Yangtze River to make up for the lack of knowledge about this area. These results provide support for the management and conservation of finless porpoises.
Lu Y +9 more
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Askey-Wilson Polynomials and Branching Laws
, 2022 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Allen Back +3 more
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Defect and degree of the Alexander polynomial
European Physical Journal C: Particles and Fields, 2022 Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simons theory.
E. Lanina, A. Morozov
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Properties of the є-expansion, Lagrange inversion and associahedra and the O (1) model
Journal of High Energy Physics, 2020 We discuss properties of the є-expansion in d = 4 − є dimensions. Using Lagrange inversion we write down an exact expression for the value of the Wilson-Fisher fixed point coupling order by order in є in terms of the beta function coefficients.
Thomas A. Ryttov
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