We characterize the solutions of the indeterminate moment problem associated with the continuous q q -Hermite polynomials when q > 1 q > 1 in terms of their Stieltjes transforms. The extremal measures are found explicitly. An analog of the Askey-Wilson integral is evaluated. It involves integrating a kernel, similar to the Askey-Wilson kernel, against any solution of the q q -Hermite moment problem, provided that certain integrability conditions hold. This led to direct evaluation of several q q -beta integrals and their discrete analogs as well as a generalization of Baileyβs 6 Ο 6 {}_6{Ο _6} , sum containing infinitely many parameters. A system of biorthogonal rational functions is also introduced.
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Ismail et al. (1994) studied this question.