International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 28131, 12 pages
On the -orthogonal polynomials and the generalized
birth and death processes
Department of Mathematics, Faculty of Science, University of Badji Mokhtar, Annaba, P.O. Box 12, Annaba 23000, Algeria
Received 16 May 2005; Revised 1 May 2006; Accepted 4 May 2006
Copyright © 2006 Zerouki Ebtissem and Boukhemis Ammar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We discuss the connections between the -orthogonal polynomials and the generalized
birth and death processes. Afterwards, we find the sufficient conditions to give an integral
representation of the transition probabilities from these processes.