The Hankel transform of a sequence obtained by series reversion

In this paper, we study the Hankel transform of a sequence defined by the series reversion of a certain rational function A(x). Using the method based on orthogonal polynomials, we give closed-form evaluations of the Hankel transform of and shifted sequences. It is also shown that the Hankel transfo...

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Bibliographic Details
Published inIntegral transforms and special functions Vol. 23; no. 11; pp. 803 - 816
Main Authors Bojičić, Radica, Petković, Marko D., Barry, Paul
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.11.2012
Taylor & Francis Ltd
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Hankel transform
Primary: 11B83
Secondary: 11C20
series reversion
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Summary:In this paper, we study the Hankel transform of a sequence defined by the series reversion of a certain rational function A(x). Using the method based on orthogonal polynomials, we give closed-form evaluations of the Hankel transform of and shifted sequences. It is also shown that the Hankel transforms satisfy certain ratio conditions which recover the sequence whose generating function is A(x). Therefore, we indicate that the term-wise ratios of Hankel transforms of shifted sequences are noteworthy objects of study, giving us more insight into the processes involved in the Hankel transform.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2011.640326