Results 211 to 220 of about 3,786,908 (243)
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On structure formulas for Wilson polynomials
Integral Transforms and Special Functions, 2015By studying various properties of some divided difference operators, we prove that Wilson polynomials are solutions of a second-order difference equation of hypergeometric type. Next, some new structure relations are deduced, the inversion and the connection problems are solved using an algorithmic method.
P. Njionou Sadjang +2 more
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SIAM Journal on Mathematical Analysis, 1987
Local symmetry (recurrence relation) techniques are a powerful tool for the efficient derivation of properties associated with families of hypergeometric and basic hypergeometric functions. Here these ideas are applied to the Wilson polynomials, a generalization of the classical orthogonal polynomials, to obtain the orthogonality relations and an ...
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Local symmetry (recurrence relation) techniques are a powerful tool for the efficient derivation of properties associated with families of hypergeometric and basic hypergeometric functions. Here these ideas are applied to the Wilson polynomials, a generalization of the classical orthogonal polynomials, to obtain the orthogonality relations and an ...
exaly +3 more sources
On the Askey-Wilson and Rogers Polynomials
Canadian Journal of Mathematics, 1988The 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, [
Ismail, Mourad E. H., Stanton, Dennis
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Integral Representations of the Wilson Polynomials and the Continuous Dual Hahn Polynomials
Advances in Applied Mathematics, 1999 Let \(\{p_n(x)\}_{n=0,1, \dots}\) denote the set of monic orthogonal polynomials, \(p_n(x)\) of degree \(n\), associated with the weight function \(w(x)\). Then it is straightforward to show \[ p_n(x)={1\over C} \int^\infty_{-\infty} dx_1w(x_1) \dots\int^\infty_{- \infty} dx_Nw(x_N) \prod^N_{l=1} (x-x_1) \prod_{1\leq ...
Katsuhisa Mimachi
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Stable Equilibria for the Roots of the Symmetric Continuous Hahn and Wilson Polynomials
, 2019We show that the gradient flows associated with a recently found family of Morse functions converge exponentially to the roots of the symmetric continuous Hahn polynomials.
J. F. van Diejen
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“Hidden symmetry” of Askey-Wilson polynomials
Theoretical and Mathematical Physics, 1991See the review in Zbl 0744.33009.
A. Zhedanov
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Constructive Approximation, 1991
The Wilson polynomials appear on top of the Askey table of hypergeometric orthogonal polynomials and thus are, together with the Racah polynomials, the most general system of hypergeometric orthogonal polynomials. They can be written as an hypergeometric \(_ 4F_ 3(1)\) in which the variable \(x\) appears in two of the numerator parameters as the ...
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The Wilson polynomials appear on top of the Askey table of hypergeometric orthogonal polynomials and thus are, together with the Racah polynomials, the most general system of hypergeometric orthogonal polynomials. They can be written as an hypergeometric \(_ 4F_ 3(1)\) in which the variable \(x\) appears in two of the numerator parameters as the ...
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Multivariable Wilson polynomials
Journal of Mathematical Physics, 1989A multivariable biorthogonal generalization of the Wilson polynomials is presented. These are four distinct families, which in a special case occur in two complex conjugate pairs, that satisfy four biorthogonality relations among them. An interesting limit case is the multivariable continuous dual Hahn polynomials.
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Askey-Wilson polynomials, kernel polynomials and association schemes
Graphs and Combinatorics, 1993For many of the classical association schemes, there are specific sets of orthogonal polynomials associated with them. When these can be found explicitly, the polynomials can be given as hypergeometric or basic hypergeometric series. A new association scheme was constructed by \textit{A. A. Ivanov}, \textit{M. E. Muzichuk} and \textit{V. A. Ustimenko} [
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On the Askey–Wilson polynomials and a $q$-beta integral
Proceedings of the American Mathematical Society, 2021Zhi-Guo Liu
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