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On Sieved Orthogonal Polynomials II: Random Walk Polynomials

Published online by Cambridge University Press:  20 November 2018

Jairo Charris  and
Mourad E. H. Ismail
Jairo Charris
Affiliation:
The National University of Colombia, Bogota, Colombia
Mourad E. H. Ismail
Affiliation:
Arizona State University, Tempe, Arizona
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A birth and death process is a stationary Markov process whose states are the nonnegative integers and the transition probabilities

(1.1)

satisfy

(1.2)

as t → 0. Here we assume βn > 0, δn + 1 > 0, n = 0, 1, …, but δ0 ≦ 0. Karlin and McGregor [10], [11], [12], showed that each birth and death process gives rise to two sets of orthogonal polynomials. The first is the set of birth and death process polynomials {Qn(x)} generated by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 2 , 01 April 1986 , pp. 397 - 415
Copyright
Copyright © Canadian Mathematical Society 1986

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