Four-term recurrences, orthogonal polynomials and Riordan arrays

Paul Barry, Aoife Hennessy

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We study constant coefficient four term recurrences for polynomials, in analogy to the three-term recurrences that are associated with orthogonal polynomials. We show that for a family of polynomials obeying such a four-term recurrence, the coefficient array is an ordinary Riordan array of a special type, and vice versa. In certain cases, it is possible to transform these polynomials into related orthogonal polynomials. We characterize the form of the production matrices of the inverse coefficient arrays.

Original languageEnglish
Pages (from-to)12.4.2
JournalJournal of Integer Sequences
Issue number4
Publication statusPublished - 26 Mar 2012


  • Four-term recur- rence
  • Hankel transform
  • Orthogonal polynomial
  • Production matrix
  • Riordan array
  • Three-term recurrence


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