{"title":"Determinantal forms and recursive relations of the Delannoy two-functional sequence","authors":"Feng Qi (祁锋), M. C. Dağlı, Wei-Shih Du","doi":"10.31219/osf.io/u683y","DOIUrl":null,"url":null,"abstract":"In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms in terms of the Hessenberg determinants and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers. This preprint has been formally published as \"Feng Qi, Muhammet Cihat Dagli, and Wei-Shih Du, Determinantal forms and recursive relations of the Delannoy two-functional sequence, Advances in the Theory of Nonlinear Analysis and its Applications, vol. 4, no. 3, pp. 184--193 (2020); available online at https://doi.org/10.31197/atnaa.772734.\"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"83 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in the Theory of Nonlinear Analysis and its Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31219/osf.io/u683y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms in terms of the Hessenberg determinants and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers. This preprint has been formally published as "Feng Qi, Muhammet Cihat Dagli, and Wei-Shih Du, Determinantal forms and recursive relations of the Delannoy two-functional sequence, Advances in the Theory of Nonlinear Analysis and its Applications, vol. 4, no. 3, pp. 184--193 (2020); available online at https://doi.org/10.31197/atnaa.772734."
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