Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind

被引：32

作者：

Guo, Bai-Ni ^{[1
]}

Qi, Feng ^{[2
,3
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China

[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China

[3] Tianjin Polytech Univ, Coll Sci, Dept Math, Tianjin 300387, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 272卷

关键词：

Explicit formula; Euler polynomial; Two-parameter Euler polynomial; Stirling number of the second kind; Identity; Exponential function; IDENTITIES; BERNOULLI;

D O I：

10.1016/j.cam.2014.05.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, the authors elementarily unify and generalize eight identities involving the functions +/- 1/e(+/- t)-1 and their derivatives. By one of these identities, the authors establish two explicit formulae for computing Euler polynomials and two-parameter Euler polynomials, which are a newly introduced notion, in terms of Stirling numbers of the second kind. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：251 / 257

页数：7

共 8 条

[1]

[Anonymous], 1972, HDB MATH FUNCTIONS F

[2]

[Anonymous], EXPLICIT FORMULAS CO

[3]

Graham Ronald L., 1994, Concrete Mathematics: A Foundation For Computer Science, V2nd

[4] Some identities and an explicit formula for Bernoulli and Stirling numbers [J].

Guo, Bai-Ni ;

Qi, Feng .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 255 :568-579

[5] Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind [J].

Qi, Feng .

FILOMAT, 2014, 28 (02) :319-327

[6] Integral representations and properties of Stirling numbers of the first kind [J].

Qi, Feng .

JOURNAL OF NUMBER THEORY, 2013, 133 (07) :2307-2319

[7] Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives [J].

Wei, Chun-Fu ;

Guo, Bai-Ni .

ABSTRACT AND APPLIED ANALYSIS, 2014,

[8] Some identities involving exponential functions and Stirling numbers and applications [J].

Xu, Ai-Min ;

Cen, Zhong-Di .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 260 :201-207

← 1 →