Some identities on degenerate hyperharmonic numbers

TL;DR

This paper explores properties, identities, and recurrence relations of degenerate hyperharmonic numbers, providing explicit formulas linking them to degenerate harmonic numbers, extending classical identities to a degenerate setting.

Contribution

It introduces a degenerate version of hyperharmonic numbers and derives explicit expressions relating them to degenerate harmonic numbers, extending known identities.

Findings

Derived explicit expression of degenerate hyperharmonic numbers in terms of degenerate harmonic numbers.

Established recurrence relations for degenerate hyperharmonic numbers.

Extended classical identities to the degenerate case.

Abstract

The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression of the degenerate hyperharmonic numbers in terms of the degenerate harmonic numbers. This is a degenerate version of the corresponding identity representing the hyperharmonic numbers in terms of harmonic numbers due to Conway and Guy.