Eulerian polynomials as moments, via exponential Riordan arrays

Details Eulerian polynomials as moments, via exponential Riordan arrays Eulerian polynomials as moments, via exponential Riordan arrays

2011-05-16

arxiv.org/abs/1105.3043v1

Mathematics

Combinatorics

12 pages

Scientific paper

Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, 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 the polynomial sequences in terms of continued fractions, and we also calculate their Hankel transforms.

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