Shell polynomials and dual birth-death processes

Erik A. van Doorn

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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 McGregorand 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.
Original languageUndefined
Pages (from-to)049
Number of pages15
JournalSymmetry, integrability and geometry : methods and applications (SIGMA)
Publication statusPublished - 18 May 2016


  • MSC-60J80
  • MSC-42C05
  • MSC-44A60
  • Orthogonal polynomials
  • EWI-27013
  • IR-100431
  • Shell polynomials
  • Stieltjes moment problem
  • Birth-death processes
  • Dual birth-death processes
  • METIS-316926
  • Similar birth-death processes

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