Askey-Wilson type functions with bound states
نویسندگان
چکیده
منابع مشابه
Askey-wilson Type Functions, with Bound States
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [19], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting...
متن کاملAskey-wilson Functions and Quantum Groups
Eigenfunctions of the Askey-Wilson second order q-difference operator for 0 < q < 1 and |q| = 1 are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra Uq(sl(2,C)). The eigenfunctions are in integral form and may be viewed as analogues of Euler’s integral representation for Gauss’ hypergeometric series. We show that for ...
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...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2006
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-006-8478-6