This article is cited in 3 papers

Ramanujan-type continuous measures for classical $q$-polynomials

N. M. Atakishiyev<sup>ab

a</sup> Institute of Physics Azerbaijan Academy of Sciences
^b National Autonomous University of Mexico, Institute of Mathematics

Abstract: 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 ${}_2\phi _1$.

Received: 01.03.1995

 English version: Theoretical and Mathematical Physics, 1995, 105:3, 1500–1508

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