New results on higher-order Daehee and Bernoulli numbers and polynomials

Advances in Difference Equations

Beih S El-Desouky¹ 

[1] Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

关键词: Daehee numbers;    Daehee polynomials;    higher-order Daehee numbers;    higher-order Daehee polynomials;    higher-order Bernoulli polynomials;    matrix representation;    05A19;    11C20;    11B73;    11T06;   

DOI  :  10.1186/s13662-016-0764-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We derive a new matrix representation for higher-order Daehee numbers and polynomials, higher-order λ-Daehee numbers and polynomials, and twisted λ-Daehee numbers and polynomials of order k. This helps us to obtain simple and short proofs of many previous results on higher-order Daehee numbers and polynomials. Moreover, we obtain recurrence relations, explicit formulas, and some new results for these numbers and polynomials. Furthermore, we investigate the relation between these numbers and polynomials and Stirling, Nörlund, and Bernoulli numbers of higher-order. Some numerical results and program are introduced using Mathcad for generating higher-order Daehee numbers and polynomials. The results of this article generalize the results derived very recently by El-Desouky and Mustafa (Appl. Math. Sci. 9(73):3593-3610, 2015).

【 授权许可】

CC BY