2011/12/07 by Radica Bojičić, Bojičić, Radica, Marko D. Petković +3
Computer Science · Mathematics · #11B83 #11C20 #11Y55 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Digital Filter Design and Implementation #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1112.1656
openalex publication_date 2011/12/07 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
This paper provides the connection between the Hankel transform and aerating\ntransforms of a given integer sequence. Results obtained are used to establish\na completely different Hankel transform evaluation of the series reversion of a\ncertain rational function Q(x) and shifted sequences, recently published in\nour paper citepart1. For that purpose, we needed to evaluate the Hankel\ntransforms of the sequences seqn\α2 Cn-\β Cn+1 and\n seqn\α2 Cn+1-\β Cn+2, where C= seqnCn is the well-known\nsequence of Catalan numbers. This generalizes the results of Cvetkovi ' c,\nRajkovi 'c and Ivkovi 'c citeCRI. Also, we need the evaluation of\nHankel-like determinants whose entries are Catalan numbers Cn and which is\nbased on the recent results of Krattenthaler citekrattCat. The results\nobtained are general and can be applied to many other Hankel transform\nevaluations.\n