New Results on Higher-Order Changhee Numbers and Polynomials

TL;DR

This paper introduces new matrix representations and formulas for higher-order Changhee numbers and polynomials, revealing their relations with Stirling, Bernoulli, and Norlund numbers, along with computational results.

Contribution

It provides novel matrix representations, simplified proofs, recurrence relations, explicit formulas, and explores connections with other special numbers.

Findings

New matrix representation for higher-order Changhee numbers and polynomials

Recurrence relations and explicit formulas derived

Relations established with Stirling, Bernoulli, and Norlund numbers

Abstract

We derive new matrix representation for higher-order changhee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on higher-order changhee numbers and polynomials. Moreover, we obtain recurrence relations, explicit formulas and some new results for these numbers and polynomials. Furthermore, we investigate the relations between these numbers and polynomials and Stirling numbers, Norlund and Bernoulli numbers of higher-order. Some numerical results using Mathcad program are introduced.