Some Properties and Generating Functions of Generalized Harmonic Numbers

Some Properties and Generating Functions of Generalized Harmonic Numbers

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 t...

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Bibliographic Details
Main Authors: Giuseppe Dattoli, Silvia Licciardi, Elio Sabia, Hari M. Srivastava
Format: Article
Language:English
Published: MDPI AG 2019-06-01
Series:Mathematics
Subjects:
umbral methods
harmonic numbers
special functions
integral representations
laplace and other integral transforms
Online Access:https://www.mdpi.com/2227-7390/7/7/577
Description
Summary: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.
ISSN:2227-7390

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