Work

Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials

Year: 2017

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1711.07100

Authors: Jiu, Lin, Shi, Diane Yahui

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2885871321

Cites: 13

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Related to: 10