Some Properties and Generating Functions of Generalized Harmonic Numbers
Date
2019
Authors
Dattoli, Giuseppe
Licciardi, Silvia
Sabia, Elio
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
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.
Description
Keywords
umbral methods, harmonic numbers, special functions, integral representations, laplace and other integral transforms
Citation
Dattoli, G., Licciardi, S., Sabia, E. & Srivastava, H.M. (2019). Some Properties and Generating Functions of Generalized Harmonic Numbers. Mathematics, 7(7), 577. https://doi.org/10.3390/math7070577