In this paper, we introduce higher-order harmonic numbers and derive their relevant properties and generating functions by using an umbral-type method. We discuss the link with recent works on the subject, and show that the combinations of umbral and other techniques (such as the Laplace and other types of integral transforms) yield a very efficient tool to explore the properties of these numbers.

Some properties and generating functions of generalized harmonic numbers

Dattoli G.;Sabia E.;
2019

Abstract

In this paper, we introduce higher-order harmonic numbers and derive their relevant properties and generating functions by using an umbral-type method. We discuss the link with recent works on the subject, and show that the combinations of umbral and other techniques (such as the Laplace and other types of integral transforms) yield a very efficient tool to explore the properties of these numbers.
Harmonic numbers; Integral representations; Laplace and other integral transforms; Special functions; Umbral methods
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12079/52183
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