Journal of Integer Sequences, Vol. 14 (2011), Article 11.9.5

Eulerian Polynomials as Moments, via Exponential Riordan Arrays

Paul Barry
School of Science
Waterford Institute of Technology


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 arrays 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.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000629 A000670 A007318 A008292 A091804 A105278 A123125 A173018.)

Received May 6 2011; revised version received September 16 2011; October 17 2011. Published in Journal of Integer Sequences, October 17 2011.

Return to Journal of Integer Sequences home page