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.
Dattoli G., Licciardi S., Sabia E., Srivastava H.M. (2019). Some properties and generating functions of generalized harmonic numbers. MATHEMATICS, 7(7) [10.3390/math7070577].
Some properties and generating functions of generalized harmonic numbers
Licciardi S.
;
2019-01-01
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.
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