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
Published inMathematics (Basel) Vol. 7; no. 7; p. 577
Main Authors Dattoli, Giuseppe, Licciardi, Silvia, Sabia, Elio, Srivastava, Hari M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2019
Subjects
Cauchy problems
Harmonic functions
harmonic numbers
integral representations
Integral transforms
laplace and other integral transforms
Mathematics
special functions
umbral methods
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ISSN2227-7390
2227-7390
DOI10.3390/math7070577

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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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math7070577