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

• F. Štampach ^[1] ; P. Šťovíček ^[1]
  1. [1] Czech Technical University in Prague

     Czech Technical University in Prague

     Chequia

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 201, Nº 1 (January 2016), 2016, págs. 48-72
• Idioma: inglés
• DOI: 10.1016/j.jat.2015.09.002
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• Resumen

  • 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.