Some identities related to degenerate r -Bell and degenerate Fubini polynomials

Abstract

Recently, Kim-Kim investigated the degenerate harmonic numbers and the degenerate hyperharmonic numbers as degenerate versions of the harmonic numbers and the hyperharmonic numbers, respectively. The aim of this paper is to study the higher-order degenerate harmonic numbers and the higher-order degenerate hyperharmonic numbers as higher-order versions for the degenerate harmonic numbers and the degenerate hyperharmonic numbers, respectively. In addition, we study the higher-order alternating degenerate hyperharmonic numbers as an 'alternating version' of the higher-order degenerate hyperharmonic numbers. In more detail, we find generating functions of them, explicit expressions for them and some relations among them for those three kinds of numbers.