General Eulerian Polynomials as Moments Using Exponential Riordan Arrays
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.
Full version: pdf,
(Concerned with sequences
Received September 26 2013;
revised version received October 13 2013.
Published in Journal of Integer Sequences, November 16 2013.
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