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arXiv · 1407.0217

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

F. Štampach·P. Šťovíček
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Abstract

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 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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F. Štampach, P. Šťovíček. 2014-07-01. The Nevanlinna parametrization for $q$-Lommel polynomials in the indeterminate case. https://doi.org/10.1016/j.jat.2015.09.002

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