Some Properties and Generating Functions of Generalized Harmonic Numbers

Mathematics

HariM. Srivastava¹  Giuseppe Dattoli²  Silvia Licciardi²  Elio Sabia² 

[1] Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy;

关键词: umbral methods;    harmonic numbers;    special functions;    integral representations;    laplace and other integral transforms;   

DOI  :  10.3390/math7070577

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown