The Hankel transform of aerated sequences

Bojičić, Radica and Petković, Marko D. and Barry, Paul (2013) The Hankel transform of aerated sequences. Integral Transforms and Special Functions, 24 (9). pp. 685-699. ISSN 1065-2469

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This paper provides the connection between the Hankel transform and aerating transforms of a given integer sequence. Two different aerating transforms are introduced and closed-form expressions are derived for the Hankel transform of such aerated sequences. Combinations of both aerating and the Hankel transforms are also considered. Our results are general and can be applied to a wide class of integer sequences. As an application, we use our tools on the sequence of shifted Catalan numbers (Cn+t)n∈ℕ0. For that purpose, we need to evaluate the Hankel and Hankel-like determinants based on the Catalan numbers. Our approach is based on the results of Gessel and Viennot [Determinants, paths, and plane partitions preprint. Available from:] and more recent results of Krattenthaler [Determinants of (generalised) Catalan numbers. J. Statist. Plann. Inference 2010; 240: 2260-2270]. We generalize a sequence obtained by the series reversion of Q(x) = x/(1 + αx + βx2) (studied in our previous paper [Bojičić R, Petković MD, Barry P. Hankel transform of a sequence obtained by series reversion. Integral Transforms Spec. Funct. DOI: 10.1080/10652469.2011.640326]) and provide the Hankel transform evaluation of that sequence and its shifted sequences.

Item Type: Article
Additional Information: Funding Information: Marko D. Petković gratefully acknowledges the support of the research project 174013 of the Serbian Ministry of Education and Science. The authors thank an anonymous reviewer, whose comments significantly improved the quality of the paper and were the motivation for some results. The authors also thank Professor Predrag M. Rajković for useful discussions on this topic.
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2603
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Date Deposited: 19 Oct 2022 23:03
Last Modified: 07 Jun 2023 18:42

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