Some cubic birth and death processes and their related orthogonal polynomials
Gilewicz, Jacek ; Leopold, Elie ; Ruffing, Andreas ; Valent, Galliano
arXiv, 0511089 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-11-28
Classification:  Mathematical Physics 
@article{0511089,
     author = {Gilewicz, Jacek and Leopold, Elie and Ruffing, Andreas and Valent, Galliano},
     title = {Some cubic birth and death processes and their related orthogonal
  polynomials},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511089}
}

Gilewicz, Jacek; Leopold, Elie; Ruffing, Andreas; Valent, Galliano. Some cubic birth and death processes and their related orthogonal
  polynomials. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511089/