RAMANUJAN-TYPE CONTINUOUS MEASURES FOR CLASSICAL Q-POLYNOMIALS

It is shown that Ramanujan-type measures for a hierarchy of classical q-orthogonal polynomials can be systematically built from simple cases of continuous q-Hermite and q(-1)-Hermite polynomials using the Berg- Ismail procedure of attaching generating functions to measures. Applic ation of this technique also leads to the evaluation, of Ramanujan-typ e integrals for Al-Salam-Chihara polynomials where 0 < q < 1, and q > 1, as well as for the product of four particular nonterminating basic hypergeometric functions 2 phi 1.