Geodesic
Eulerian polynomials as moments, via exponential Riordan arrays
Journal of integer sequences, Tome 14 (2011) no. 9.

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Summary: 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 arrays 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.
Classification : 11B83, 33C45, 42C05, 15B36, 15B05, 11C20
Keywords: Eulerian number, Eulerian polynomial, Euler's triangle, exponential Riordan array, orthogonal polynomials, moments, Hankel transform 
@article{JIS_2011__14_9_a3,
     author = {Barry, Paul},
     title = {Eulerian polynomials as moments, via exponential {Riordan} arrays},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {14},
     number = {9},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_9_a3/}
}
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Barry, Paul. Eulerian polynomials as moments, via exponential Riordan arrays. Journal of integer sequences, Tome 14 (2011) no. 9. http://geodesic.mathdoc.fr/item/JIS_2011__14_9_a3/