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Product formulas for basic hypergeometric series by evaluations of Askey--Wilson polynomials [PDF]
Howard S. Cohl, Michael Schlosser
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Wilson polynomials and some continued fractions of Ramanujan [PDF]
Rocky Mountain Journal of Mathematics, 1991 openaire +2 more sources
On structure formulas for Wilson polynomials [PDF]
Integral Transforms and Special Functions, 2015 By 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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Asymptotics of the Wilson polynomials
Analysis and Applications, 2019In 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. Infinite asymptotic expansions are derived for these polynomials in various cases, for instance, (i) when the variable ...
Roderick Wong +2 more
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On the Askey-Wilson polynomials
Constructive Approximation, 1992Main properties of the Askey-Wilson polynomials are compactly given on the basis of a generalization of Hahn's approach.
Natig M. Atakishiyev, Sergei K. Suslov
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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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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 ...
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Constructive Approximation, 1991
From a contiguous relation obtained by Wilson for terminating 2-balanced very well-poised9 F 8 hypergeometric functions of unit argument, we derive a pair of three term recurrence relations for very well-poised7 F 6's. From these we obtain solutions to the recurrence relation for associated Wilson polynomials and spectral properties of the ...
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From a contiguous relation obtained by Wilson for terminating 2-balanced very well-poised9 F 8 hypergeometric functions of unit argument, we derive a pair of three term recurrence relations for very well-poised7 F 6's. From these we obtain solutions to the recurrence relation for associated Wilson polynomials and spectral properties of the ...
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?Hidden symmetry? of Askey-Wilson polynomials [PDF]
Theoretical and Mathematical Physics, 1991 We have shown that the Askey-Wilson polynomials of general form are generated by the algebra AW(3), which has a fairly simple structure and is the q-analog of a Lie algebra with three generators. The main properties of these polynomials (weight function, recursion relation, etc.) can be obtained directly from analysis of the representations of the ...
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Askey-Wilson polynomials, kernel polynomials and association schemes
Graphs and Combinatorics, 1993The eigenvalues of the classical association schemes are given by certain Askey-Wilson polynomials (or limiting cases). Kernel polynomials of the Askey-Wilson polynomials are also Askey-Wilson polynomials. We determine when both the Askey-Wilson polynomials and their kernels are the eigenvalues for known association schemes.
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