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Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials (1711.07100v4)
Published 19 Nov 2017 in math.CO and math.PR
Abstract: We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are Meixner-Pollaczek polynomials with certain arguments and constant factors. Moreover, through a general connection between moments of random variables and the generalized Motzkin numbers, we can obtain a new recurrence formula and a matrix representation for the higher-order Euler polynomials, interpreting them as weighted lattice paths.
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