Some Properties and Generating Functions of Generalized Harmonic Numbers

Giuseppe Dattoli, Silvia Licciardi, Elio Sabia and Hari M. Srivastava
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Giuseppe Dattoli: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Silvia Licciardi: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Elio Sabia: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

Mathematics, 2019, vol. 7, issue 7, 1-12

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.

Keywords: umbral methods; harmonic numbers; special functions; integral representations; laplace and other integral transforms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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