{"title":"Identities between harmonic, hyperharmonic and Daehee numbers.","authors":"Seog-Hoon Rim, Taekyun Kim, Sung-Soo Pyo","doi":"10.1186/s13660-018-1757-0","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we present some identities relating the hyperharmonic, the Daehee and the derangement numbers, and we derive some nonlinear differential equations from the generating function of a hyperharmonic number. In addition, we use this differential equation to obtain some identities in which the hyperharmonic numbers and the Daehee numbers are involved.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1757-0","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1757-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/7/11 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 13
Abstract
In this paper, we present some identities relating the hyperharmonic, the Daehee and the derangement numbers, and we derive some nonlinear differential equations from the generating function of a hyperharmonic number. In addition, we use this differential equation to obtain some identities in which the hyperharmonic numbers and the Daehee numbers are involved.
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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