Some cubic birth and death processes and their related orthogonal polynomials

Details Some cubic birth and death processes and their related orthogonal polynomials Some cubic birth and death processes and their related orthogonal polynomials

2005-11-28

arxiv.org/abs/math-ph/0511089v1

Constructive Approximation 24 (2006) 71-89

Physics

Mathematical Physics

latex2e, 17 pages

Scientific paper

10.1007/s00365-005-0604-y

The orthogonal polynomials with recurrence relation \[(\la\_n+\mu\_n-z) F\_n(z)=\mu\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z)\] with two kinds of cubic transition rates $\la\_n$ and $\mu\_n,$ 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 the asymptotics of the Nevanlinna matrices in the complex plane.

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