Some Properties and Generating Functions of Generalized Harmonic Numbers
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 t...
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MDPI AG
2019-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/7/577 |
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doaj-b34e7aa6d66e47488a17547de8a97c6b2020-11-24T22:09:22ZengMDPI AGMathematics2227-73902019-06-017757710.3390/math7070577math7070577Some Properties and Generating Functions of Generalized Harmonic NumbersGiuseppe Dattoli0Silvia Licciardi1Elio Sabia2Hari M. Srivastava3ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, ItalyENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, ItalyENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, ItalyDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaIn 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.https://www.mdpi.com/2227-7390/7/7/577umbral methodsharmonic numbersspecial functionsintegral representationslaplace and other integral transforms |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Giuseppe Dattoli Silvia Licciardi Elio Sabia Hari M. Srivastava |
| spellingShingle |
Giuseppe Dattoli Silvia Licciardi Elio Sabia Hari M. Srivastava Some Properties and Generating Functions of Generalized Harmonic Numbers Mathematics umbral methods harmonic numbers special functions integral representations laplace and other integral transforms |
| author_facet |
Giuseppe Dattoli Silvia Licciardi Elio Sabia Hari M. Srivastava |
| author_sort |
Giuseppe Dattoli |
| title |
Some Properties and Generating Functions of Generalized Harmonic Numbers |
| title_short |
Some Properties and Generating Functions of Generalized Harmonic Numbers |
| title_full |
Some Properties and Generating Functions of Generalized Harmonic Numbers |
| title_fullStr |
Some Properties and Generating Functions of Generalized Harmonic Numbers |
| title_full_unstemmed |
Some Properties and Generating Functions of Generalized Harmonic Numbers |
| title_sort |
some properties and generating functions of generalized harmonic numbers |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2019-06-01 |
| description |
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. |
| topic |
umbral methods harmonic numbers special functions integral representations laplace and other integral transforms |
| url |
https://www.mdpi.com/2227-7390/7/7/577 |
| work_keys_str_mv |
AT giuseppedattoli somepropertiesandgeneratingfunctionsofgeneralizedharmonicnumbers AT silvialicciardi somepropertiesandgeneratingfunctionsofgeneralizedharmonicnumbers AT eliosabia somepropertiesandgeneratingfunctionsofgeneralizedharmonicnumbers AT harimsrivastava somepropertiesandgeneratingfunctionsofgeneralizedharmonicnumbers |
| _version_ |
1725812259900358656 |