Degenerate hyperharmonic polynomials and numbers

Abstract

This paper explores new identities and relations for degenerate hyperharmonic numbers and degenerate hyperharmonic polynomials, which are respectively a degenerate version of hyperharmonic numbers and a polynomial extension of the degenerate hyperharmonic numbers. Key results include expressing degenerate hyperharmonic numbers and polynomials in terms of finite sums involving unsigned degenerate Stirling numbers of the first kind, degenerate Bernoulli polynomials, and other related numbers. We also derive a recurrence relation for the degenerate hyperharmonic numbers and a closed-form expression for an alternating sum involving degenerate harmonic numbers.