Identities involving degenerate harmonic and degenerate hyperharmonic numbers

TL;DR

This paper explores properties, recurrence relations, and identities involving degenerate harmonic and hyperharmonic numbers, connecting them with degenerate Stirling numbers, Daehee numbers, and derangements.

Contribution

It introduces new properties and identities for degenerate harmonic and hyperharmonic numbers, linking them with other degenerate combinatorial numbers.

Findings

Derived new recurrence relations for degenerate harmonic numbers.

Established identities connecting degenerate hyperharmonic numbers with degenerate Stirling numbers.

Extended the theory of degenerate harmonic numbers through novel properties.

Abstract

Harmonic numbers have been studied since antiquity, while hyperharmonic numbers were intoduced by Conway and Guy in 1996. The degenerate harmonic numbers and degenerate hyperharmonic numbers are their respective degenerate versions. The aim of this paper is to further investigate some properties, recurrence relations and identities involving the degenerate harmonic and degenerate hyperharmonic numbers in connection with degenerate Stirling numbers of the first kind, degenerate Daehee numbers and degenerate derangements.