# Associated polynomials and birth-death processes

Erik A. van Doorn

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## Abstract

We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to applications in the setting of birth-death processes. In particular, we relate the supports of the two measures, and their moments of positive and negative orders. Our results indicate how the prevalence of recurrence or $\alpha$-recurrence in a birth-death process can be recognized from certain properties of an associated measure.
Original language English Enschede University of Twente, Department of Applied Mathematics Published - 2001

### Publication series

Name Memorandum / Department of Applied Mathematics Department of Applied Mathematics, University of Twente 1581 0169-2690

• MSC-42C05
• EWI-3401
• IR-65768
• MSC-60J80