Explicit Formulas for Special Values of the Bell Polynomials of the Second Kind and for the Euler Numbers and Polynomials

被引：42

作者：

Qi, Feng ^{[1
,2
,3
]}

Guo, Bai-Ni ^{[4
]}

机构：

[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China

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

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

[4] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454010, Henan, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2017年 / 14卷 / 03期

关键词：

Explicit formula; special value; Bell polynomial of the second kind; Euler number; Euler polynomial; double sum; weighted Stirling number; property; WEIGHTED STIRLING NUMBERS; BERNOULLI NUMBERS; 1ST; EXPRESSIONS; TERMS;

D O I：

10.1007/s00009-017-0939-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, the authors establish by two approaches several explicit formulas for special values of the Bell polynomials of the second kind, derive explicit formulas for the Euler numbers and polynomials in terms of double sums and the weighted Stirling numbers, and find a property for special values of the Bell polynomials of the second kind.

引用

页数：14

共 21 条

[1] THE R-STIRLING NUMBERS [J].

BRODER, AZ .

DISCRETE MATHEMATICS, 1984, 49 (03) :241-259

[2]

CARLITZ L, 1980, FIBONACCI QUART, V18, P242

[3]

CARLITZ L, 1980, FIBONACCI QUART, V18, P147

[4]

Carlitz L., 1959, Math. Mag, V32, P247, DOI DOI 10.2307/3029225

[5]

Comtet L., 1974, ADV COMBINATORICS AR

[6]

Guo B. - N., 2015, TECHNICAL REPORT

[7]

Guo B. -N., 2015, J. Anal. Number Theory, V3, P27

[8] AN EXPLICIT FORMULA FOR BERNOULLI POLYNOMIALS IN TERMS OF r-STIRLING NUMBERS OF THE SECOND KIND [J].

Guo, Bai-Ni ;

Mezo, Istavan ;

Qi, Feng .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2016, 46 (06) :1919-1923

[9] Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind [J].

Guo, Bai-Ni ;

Qi, Feng .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 272 :251-257

[10] DOUBLE SERIES FOR BERNOULLI AND EULER NUMBERS [J].

HIGGINS, J .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 1970, 2 (OCT) :722-+

← 1 2 3 →