Results 21 to 30 of about 45,941 (258)
Non-symmetric Jacobi and Wilson type polynomials [PDF]
International Mathematics Research Notices, 2005 Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure $|c(\lam)|^{-2}d\lam$.
Lizhong Peng, Genkai Zhang
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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.
Odake, Satoru, Sasaki, Ryu
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Multi-indexed Wilson and Askey–Wilson 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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Equilibrium positions, shape invariance and Askey–Wilson polynomials [PDF]
Journal of Mathematical Physics, 2005 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. The corresponding single particle quantum version, which is a typical example of “discrete” quantum mechanical systems with a q-shift type kinetic term, is ...
Satoru Odake, Ryu Sasaki
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On the Askey-Wilson and Rogers Polynomials [PDF]
Canadian Journal of Mathematics, 1988 The q-shifted factorial (a)n or (a; q)n isand an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials1.1where1.2and1.3We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [
Mourad E. H. Ismail, Dennis Stanton
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The structure relation for Askey–Wilson polynomials [PDF]
Journal of Computational and Applied Mathematics, 2006 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n+1.
Tom H. Koornwinder
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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.
Gisonni, M., Grava, T., Ruzza, G.
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Multi-Decadal Analysis on the Impact of Climate Change, Genetic Gain, Cultivar Type, and Harvest Timing on Main and Ratoon Rice Yield and Quality. [PDF]
Glob Chang BiolAn analysis of 33 years of data estimated the impact of climate change, genetic gain, cultivar type, and harvest timing on rice yield and quality. Degree‐days (˚D) and atmospheric [CO2] have increased 11.6% and 18.4%, respectively. Several climatic variables have impacted grain yield, some positively and some negatively, and many have reduced grain ...
Wilson LT, Samonte SOPB, Yang Y.
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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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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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