Some orthogonal very well poised -functions
نویسندگان
چکیده
منابع مشابه
Some Orthogonal Very-well-poised 8'7-functions That Generalize Askey{wilson Polynomials
In a recent paper Ismail et al. (Algebraic Methods and q-Special Functions (J.F. van Diejen and L. Vinet, eds.) CRM Proceding and Lecture Notes, Vol. 22, American Mathematical Society, 1999, pp. 183–200) have established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Dick Askey (private communication) suggested that the “Bessel-type...
متن کاملSome Remarks on Very - Well - Poised 8 φ 7 Series
Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as very-well-poised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new der...
متن کاملOrthogonality of Very Well-poised Series
Rodrigues formulas for very well-poised basic hypergeometric series of any order are given. Orthogonality relations are found for rational functions which generalize Rahman’s 10φ9 biorthogonal rational functions. A pair of orthogonal rational functions of type RII is identified. Elliptic analogues of some of these results are also included.
متن کاملUvA - DARE ( Digital Academic Repository ) Some remarks on very - well - poised 87 series
Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as very-well-poised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new der...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1997
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/30/16/027