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 the continuous $q$-Hermite and $q^{-1}$-Hermite polynomials by using the Berg–Ismail procedure of attaching generating functions to measures. The application of this technique leads also to the evaluation of Ramanujan-type integrals for the Al-Salam–Chihara polynomials both when $0<q<1$ and $q>1$, as well as for the product of four particular nonterminating basic hypergeometric functions ${}_2\phi _1$.