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Some Properties and Generating Functions of Generalized Harmonic Numbers

Author

Listed:
  • 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
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

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.

Suggested Citation

  • Giuseppe Dattoli & Silvia Licciardi & Elio Sabia & Hari M. Srivastava, 2019. "Some Properties and Generating Functions of Generalized Harmonic Numbers," Mathematics, MDPI, vol. 7(7), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:577-:d:244051
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    Cited by:

    1. Hao Guan & Sibel Koparal & Neşe Ömür & Waseem Ahmad Khan, 2023. "q -Analogs of H n , m r σ and Their Applications," Mathematics, MDPI, vol. 11(19), pages 1-11, October.

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