Some cubic birth and death processes and their related orthogonal polynomials

Abstract

The orthogonal polynomials with recurrence relation (λn + μn − z)Fn(z) = μn+1 Fn+1(z) + λn−1 Fn−1(z) with two kinds of cubic transition rates λn and μn, corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes of polynomials, which enable us to compute their Nevanlinna matrices. We discuss… (More)

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Cite this paper

@inproceedings{Gilewicz2005SomeCB, title={Some cubic birth and death processes and their related orthogonal polynomials}, author={Jacek Gilewicz and Andreas Ruffing}, year={2005} }