Recently Ismail, Masson and Suslov established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Askey suggested that the 'Bessel-type orthogonality' found in the above paper at the 2φ1-level really has a general character and can be extended up to the 8φ7-level. Very well poised 8φ7-fuctions are known as a nonterminating version of the classical Askey-Wilson polynomials. In this paper we prove Askey's conjecture and discuss some properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very well poised 87-function was recently found by Askey, Rahman and Suslov.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)