Geodesic
Shell Polynomials and Dual Birth-Death Processes
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper aims to clarify certain aspects of the relations between birth-death processes, measures solving a Stieltjes moment problem, and sets of parameters defining polynomial sequences that are orthogonal with respect to such a measure. Besides giving an overview of the basic features of these relations, revealed to a large extent by Karlin and McGregor, we investigate a duality concept for birth-death processes introduced by Karlin and McGregor and its interpretation in the context of shell polynomials and the corresponding orthogonal polynomials. This interpretation leads to increased insight in duality, while it suggests a modification of the concept of similarity for birth-death processes.
Keywords: orthogonal polynomials; birth-death processes; Stieltjes moment problem; shell polynomials; dual birth-death processes; similar birth-death processes. 
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     author = {Erik A. van Doorn},
     title = {Shell {Polynomials} and {Dual} {Birth-Death} {Processes}},
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Erik A. van Doorn. Shell Polynomials and Dual Birth-Death Processes. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a48/

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