The ``classical'' Laurent biorthogonal polynomials (Q1298812)

In this paper an analogue of the Hahn theorem for Laurent biorthogonal polynomials (LBP) \(P_n(z)\) is studied. Necessary and sufficient conditions for derivatives \(\widetilde P_n(z)= (n+1)^{-1} P_{n+1}'(z)\) are also obtained. These conditions are derived as a linear second-order difference equation for the moments. Some special examples of such LBP which are different from the well known classical LBP are considered. Lastly the theory of spectral transformations of these polynomials is developed which is crucial in the study of LBP belonging to the Hahn class.