Journal of Integer Sequences, Vol. 16 (2013), Article 13.9.6

General Eulerian Polynomials as Moments Using 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 general Eulerian polynomials, as defined by Xiong, Tsao and Hall, are moment sequences for simple families of orthogonal polynomials, which we characterize in terms of their three-term recurrence. We obtain the generating functions of this polynomial sequence in terms of continued fractions, and we also calculate the Hankel transforms of the polynomial sequence. We indicate that the polynomial sequence can be characterized by the further notion of generalized Eulerian distribution first introduced by Morisita. We finish with examples of related Pascal-like triangles.

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(Concerned with sequences A000165 A000354 A001710 A007047 A007318 A008290 A046802 A060187 A080253.)

Received September 26 2013; revised version received October 13 2013. Published in Journal of Integer Sequences, November 16 2013.

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