Combinatorial identities involving degenerate harmonic and hyperharmonic numbers

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

“…For those three kinds of numbers, we investigated generating functions of them, explicit expressions for them and some relations among them. We suggested an open problem about expressing the degenerate hyperharmonic numbers of order α in terms of the degenerate harmonic numbers of order α, which is possible for α = 1 (see (11), (39)).…”

“…Carlitz initiated (see [4]) the study of degenerate Bernoulli and degenerate Euler numbers and polynomials as degenerate versions of Bernoulli and Euler numbers and polynomials. Recently, this pioneering work regained interests of some mathematicians, various degenerate versions of quite a few special numbers and polynomials were investigated and some interesting arithmetical and combinatorial results were obtained along with some of their applications to other disciplines (see [9][10][11][12][13] and the references therein). For example, Kim-Kim investigated the degenerate harmonic numbers and the degenerate hyperharmonic numbers as degenerate versions of the harmonic numbers and the hyperharmonic numbers, respectively (see [10,11]).…”