Some cubic birth and death processes and their related orthogonal polynomials

Jacek Gilewicz; Elie Leopold; Andreas Ruffing; Galliano Valent

hal-00014570, version 1

Some cubic birth and death processes and their related orthogonal polynomials

Jacek Gilewicz ¹, Elie Leopold ¹, Andreas Ruffing ², Galliano Valent () ³

Constructive Approximation 24 (2006) 71-89

Abstract: 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.

1: Centre de Physique Théorique (CPT)
CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var
2: Zentrum Mathematik (TUM)
Technische Universitat Munchen
3: Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
CNRS : UMR7589 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot

hal-00014570, version 1
http://hal.archives-ouvertes.fr/hal-00014570
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From: Galliano Valent <>
Submitted on: Monday, 28 November 2005 13:05:11
Updated on: Monday, 2 October 2006 12:50:23

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arXiv: math-ph/0511089

DOI: 10.1007/s00365-005-0604-y

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