Some orthogonal very well poised ₈φ₇-functions

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.