Some identities of degenerate harmonic and degenerate hyperharmonic numbers arising from umbral calculus

Abstract

Hyperharmonic numbers were introduced by Conway and Guy (The Book of Numbers, Copernicus, New York, 1996), whereas harmonic numbers have been studied since antiquity. Recently, the degenerate hyperharmonic and degenerate harmonic numbers were introduced as their respective degenerate versions. The aim of this article is to further investigate some properties and identities involving the degenerate hyperharmonic numbers and degenerate harmonic numbers. Especially, we derive some identities by making use of the transfer formula for associated sequences from umbral calculus.

Keywords

• degenerate harmonic number
• degenerate hyperharmonic number
• umbral calculus
• 05a40
• 11b73
• 11b83