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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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On Some Limit Cases of Askey–Wilson Polynomials
Journal of Approximation Theory, 1998 The authors derive the classical orthogonality relations and norm evaluations for the \(q\)-Racah and \(q\)-Jacobi polynomials by taking limits in the orthogonality relations and norm evaluations for the Askey-Wilson polynomials [\textit{R. Askey} and \textit{J. Wilson}, Mem. Am. Math. Soc. 54, No. 319, 1-55 (1985; Zbl 0572.33012)].
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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European Journal of Personality, EarlyView., 2020 Abstract Few studies have examined birth order effects on personality in countries that are not Western, educated, industrialized, rich, and democratic (WEIRD). However, theories have generally suggested that interculturally universal family dynamics are the mechanism behind birth order effects, and prominent theories such as resource dilution would ...
Laura J. Botzet +2 more
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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]
, 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
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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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A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the
Victor J. W. Guo +3 more
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Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
Nuclear Physics B, 2022 We have recently proposed [1] a powerful method for computing group factors of the perturbative series expansion of the Wilson loop in the Chern-Simons theory with SU(N) gauge group.
E. Lanina, A. Sleptsov, N. Tselousov
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