Generalized Stirling numbers, exponential Riordan arrays and orthogonal polynomials

Aoife Hennessy, Paul Barry

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of these Riordan arrays. Generalized Bell numbers are also defined, again depending on two parameters, and we determine the Hankel transform of these numbers.

Original languageEnglish
Pages (from-to)11.8.2
JournalJournal of Integer Sequences
Volume14
Issue number8
Publication statusPublished - 2011

Keywords

  • Bell number
  • Hankel transform
  • Integer sequence
  • Orthogonal polynomial
  • Riordan array
  • Stirling number

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