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

By B. El-Desouky, A. Mustafa. 2015

47 citations recorded by the source corpus.

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).

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/6149611e6729a7bacfff32b734f7f215df187720

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Degenerate polyexponential functions and degenerate Bell polynomials (2020, background): “ential functions and the new type degenerate Bell polynomials. 1. INTRODUCTION It is well known that the Stirling numbers of the second kind are deﬁned by (1) xn = n ∑ l=0 S 2(n,l)(x) l, (n ≥0), (see [4,6,8,12,22]), where (x) 0 =1, (x) n =x(x−1)···(x−n+1), (n ≥1). From (1), we note that (2) 1 k! (et”