The Roman harmonic numbers revisited

Two decades ago, Steven Roman, Daniel E. Loeb and Gian-Carlo Rota introduced a family of harmonic numbers in their study of harmonic logarithms. We propose to refer to those numbers as {\it Roman harmonic numbers}. With the purpose of revitalizing the study of these mathematical objects, we recall h...

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Bibliographic Details
Published in:arXiv.org 2017-08
Main Author: Sesma, Javier
Format: Article
Language:English
Subjects:
Logarithms
Sum rules
Online Access:Get full text
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Summary:Two decades ago, Steven Roman, Daniel E. Loeb and Gian-Carlo Rota introduced a family of harmonic numbers in their study of harmonic logarithms. We propose to refer to those numbers as {\it Roman harmonic numbers}. With the purpose of revitalizing the study of these mathematical objects, we recall here their known properties and unveil additional ones. An integral representation, several generating relations, and a collection of sum rules involving those numbers are presented. It is also shown that higher derivatives of the Pochhammer and reciprocal Pochhammer symbols are easily expressed in terms of Roman harmonic numbers.
ISSN:2331-8422
DOI:10.48550/arxiv.1702.03718