Some orthogonal very well poised -functions

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...

Some 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...

Orthogonality 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.

UvA - 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...

Multiple-integral Representations of Very-well-poised Hypergeometric Series