منابع مشابه
Nonsymmetric Askey-Wilson polynomials and Q-polynomial distance-regular graphs
In his famous theorem (1982), Douglas Leonard characterized the q-Racah polynomials and their relatives in the Askey scheme from the duality property of Q-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the q-Racah polynomials in the above situation. Let Γ denote a Q-polynomial distance-regular graph that contains a Delsarte clique C. Assume ...
متن کاملBootstrapping and Askey-wilson Polynomials
Abstract. The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coe cients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special c...
متن کاملThe Associated Askey-wilson Polynomials
We derive some contiguous relations for very well-poised 8<^7 series and use them to construct two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials. We then use these solutions to find explicit representations of two families of associated Askey-Wilson polynomials. We identify the corresponding continued fractions as quotients of tw...
متن کاملThe Universal Askey–Wilson Algebra
Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. We define an associative F-algebra ∆ = ∆q by generators and relations in the following way. The generators are A, B, C. The relations assert that each of A+ qBC − q−1CB q2 − q−2 , B + qCA− q−1AC q2 − q−2 , C + qAB − q−1BA q2 − q−2 is central in ∆. We call ∆ the universal Askey–Wilson algebra. We discuss how ∆ is related to the orig...
متن کاملMoments of Askey-Wilson polynomials
New formulas for the n moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured. Résumé. Nous présentons de nouvelles formules pour les n-moments μn(a, b, c, d...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2012
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.7761