*Article* **Some Properties and Generating Functions of Generalized Harmonic Numbers**

#### **Giuseppe Dattoli 1, Silvia Licciardi 1,\*, Elio Sabia 1 and Hari M. Srivastava 2,3**


Received: 5 May 2019; Accepted: 24 June 2019; Published: 28 Junbe

**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

**MSC:** 05A40, 44A99, 47B99; 11A99; 33C52, 33C65, 33C99, 33B10, 33B15; 44A05, 44A20; 44A10, 44A15
