General eulerian polynomials as moments using exponential riordan arrays

Barry, Paul (2013) General eulerian polynomials as moments using exponential riordan arrays. Journal of Integer Sequences, 16 (9). pp. 1-15. ISSN 1530-7638

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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.

Item Type: Article
Additional Information: Publisher Copyright: © 2014, Journal of Integer Sequences. All rights reserved.
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2607
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Depositing User: Admin SSL
Date Deposited: 19 Oct 2022 23:07
Last Modified: 04 Feb 2023 00:01

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