Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials
Combinatorics
2018-08-14 v4 Probability
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.
Cite
@article{arxiv.1711.07100,
title = {Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials},
author = {Lin Jiu and Diane Yahui Shi},
journal= {arXiv preprint arXiv:1711.07100},
year = {2018}
}