{"title":"Catalan and Motzkin integral\n representations","authors":"Peter N. McCalla, A. Nkwanta","doi":"10.1090/conm/759/15270","DOIUrl":null,"url":null,"abstract":"We present new proofs of eight integral representations of the Catalan numbers. Then, we create analogous integral representations of the Motzkin numbers and obtain new results. Most integral representations of counting sequences found in the literature are proved by using advanced mathematical techniques. All integral representations in this paper are proved by using standard techniques from integral calculus. Thus, we provide a more simplistic approach of proving integral representations of the Catalan and Motzkin numbers.","PeriodicalId":351002,"journal":{"name":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/759/15270","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We present new proofs of eight integral representations of the Catalan numbers. Then, we create analogous integral representations of the Motzkin numbers and obtain new results. Most integral representations of counting sequences found in the literature are proved by using advanced mathematical techniques. All integral representations in this paper are proved by using standard techniques from integral calculus. Thus, we provide a more simplistic approach of proving integral representations of the Catalan and Motzkin numbers.