Orthogonal polynomials and connection to generalized Motzkin numbers for higher-order Euler polynomials

被引：3

作者：

Jiu, Lin ^{[1
]}

Shi, Diane Yahui ^{[2
]}

机构：

[1] Dalhousie Univ, Dept Math & Stat, 6316 Coburg Rd, Halifax, NS B3H 4R2, Canada

[2] Tianjin Univ, Sch Math, 92 Weijin Rd, Tianjin 300072, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2019年 / 199卷

基金：

美国国家科学基金会;

关键词：

Higher-order Euler polynomials; Orthogonal polynomial; Meixner-Pollaczek polynomial; Generalized Motzkin number; BERNOULLI;

D O I：

10.1016/j.jnt.2018.11.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are the Meixner-Pollaczek polynomials with certain arguments and constant factors. Moreover, we obtain a connection to the generalized Motzkin number, which leads to a new recurrence formula and a matrix representation for the higher-order Euler polynomials. Analogue on Bernoulli polynomials is presented in the end. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：389 / 402

页数：14

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