Eulerian polynomials as moments, via exponential Riordan arrays

Barry, Paul (2011) Eulerian polynomials as moments, via exponential Riordan arrays. Journal of Integer Sequences, 14 (9). ISSN 1530-7638

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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.

Item Type: Article
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2607
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Depositing User: Admin SSL
Date Deposited: 19 Oct 2022 23:02
Last Modified: 31 Jul 2023 19:15

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