Eulerian polynomials as moments, via exponential Riordan arrays

Abstract

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.

12 pages

Cited by in corpus (10)

• Relations between cumulants in noncommutative probability
• Central factorial numbers associated with sequences of polynomials
• The $1/k$-Eulerian Polynomials as Moments, via Exponential Riordan Arrays
• Generalized Eulerian Triangles and Some Special Production Matrices
• Strong q-log-convexity of the Eulerian polynomials of Coxeter groups
• Eulerian-Dowling Polynomials as Moments, Using Riordan Arrays
• Three Études on a sequence transformation pipeline
• Some identities of Eulerian polynomials arising from nonlinear differential equations
• Series reversion with Jacobi and Thron continued fractions
• A note on Hermite polynomials