The Nevanlinna parametrization for q-Lommel polynomials in the indeterminate case

The Hamburger moment problem for the q -Lommel polynomials which are related to the Hahn-Exton q -Bessel function is known to be indeterminate for a certain range of parameters. In this paper, the Nevanlinna parametrization for the indeterminate case is provided in an explicit form. This makes it possible to describe all N-extremal measures of orthogonality. Moreover, a linear and a quadratic recurrence relation are derived for the moment sequence, and the asymptotic behavior of the moments for large powers is obtained with the aid of appropriate estimates.

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