Abstract
We characterize the solutions of the indeterminate moment problem associated with the continuousqq-Hermite polynomials whenq>1q > 1in 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 theqq-Hermite moment problem, provided that certain integrability conditions hold. This led to direct evaluation of severalqq-beta integrals and their discrete analogs as well as a generalization of Bailey’s6ψ6{}_6{\psi _6}, sum containing infinitely many parameters. A system of biorthogonal rational functions is also introduced.
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