Eulerian polynomials as moments, via exponential Riordan arrays

Paul Barry

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the Eulerian polynomials and the shifted Eulerian polynomials are moment sequences for a simple family of orthogonal polynomials. The coefficient ar-rays of these families of orthogonal polynomials are shown to be exponential Riordan arrays. Using the theory of orthogonal polynomials we are then able to characterize the generating functions of the Eulerian and shifted Eulerian polynomials in continued fraction form, and to calculate their Hankel transforms.

Original languageEnglish
JournalJournal of Integer Sequences
Issue number9
Publication statusPublished - 2011


  • Euler's triangle
  • Eulerian number
  • Eulerian polynomial
  • Exponential riordan array
  • Hankel transform
  • Moments
  • Orthogonal polynomials


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