New Results on Higher-Order Daehee and Bernoulli Numbers and Polynomials

TL;DR

This paper introduces new matrix representations and formulas for higher-order Daehee and Bernoulli numbers and polynomials, generalizing recent results and exploring their relations with Stirling, Nörlund, and Bernoulli numbers.

Contribution

It provides novel matrix representations, recurrence relations, explicit formulas, and generalizations for higher-order Daehee and Bernoulli numbers and polynomials.

Findings

Derived new matrix representations for higher-order Daehee and Bernoulli numbers.

Established recurrence relations and explicit formulas.

Explored relations with Stirling, Nörlund, and Bernoulli numbers.

Abstract

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-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 obtained recurrence relation, explicit formulas and some new results for these numbers and polynomials. Furthermore, we investigated the relation between these numbers and polynomials and Stirling numbers, Norlund and Bernoulli numbers of higher order. The results of this article gives a generalization of the results derived very recently by El-Desouky and Mustafa [6].