1997/07/01 by Suslov, Sergei K.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/9707213
In a recent paper Ismail, Masson, and Suslov have established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Dick Askey suggested that the ``Bessel-type orthogonality'' at the 2φ1-level has really a general character and can be extended up to the 8φ7-level. Very-well-poised 8φ7-functions are known as a nonterminating version of the classical Askey--Wilson polynomials. Askey's congecture has been proved by the author. In the present paper we discuss in details some properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very-well-poised 8φ7-function was recently found by Askey, Rahman, and Suslov.