{"title":"Generalized Central Factorial Numbers with Odd Arguments","authors":"Youmna H. Zaid, F. Shiha, B. El-Desouky","doi":"10.4236/ojmsi.2020.83005","DOIUrl":null,"url":null,"abstract":"In this \npaper, we consider r-generalization of \nthe central factorial numbers with odd arguments of the first and second kind. Mainly, \nwe obtain various identities and properties related to these numbers. Matrix representation \nand the relation between these numbers and Pascal matrix are given. Furthermore, \nthe distributions of the signless r-central factorial numbers are derived. In addition, \nconnections between these numbers and the Legendre-Stirling numbers are given.","PeriodicalId":56990,"journal":{"name":"建模与仿真(英文)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"建模与仿真(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/ojmsi.2020.83005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this
paper, we consider r-generalization of
the central factorial numbers with odd arguments of the first and second kind. Mainly,
we obtain various identities and properties related to these numbers. Matrix representation
and the relation between these numbers and Pascal matrix are given. Furthermore,
the distributions of the signless r-central factorial numbers are derived. In addition,
connections between these numbers and the Legendre-Stirling numbers are given.