Note on Askey-Wilson $q$-Contour Integral Formula
نویسندگان
چکیده
منابع مشابه
An Expansion Formula for the Askey-Wilson Function
The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey-Wilson second order q-difference operator. The kernel is called the Askey-Wilson function. In this paper an explicit expansion formula for the Askey-Wilson function in terms of Askey-Wilson polynomials is proven. With this expansion form...
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We nd the adjoint of the Askey-Wilson divided di erence operator with respect to the inner product on L 2 ( 1; 1; (1 x 2 ) 1=2 dx) de ned as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic de...
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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 کاملOn a Family of Integrals that extend the Askey-Wilson Integral
We study a family of integrals parameterised by N = 2, 3, . . . generalising the Askey-Wilson integral N = 2 which has arisen in the theory of q-analogs of monodromy preserving deformations of linear differential systems and in theory of the Baxter Q operator for the XXZ open quantum spin chain. These integrals are particular examples of moments defined by weights generalising the Askey-Wilson ...
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...
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2014
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v6n2p59