The Hankel transform of a sequence obtained by series reversion

Radica Bojičić, Marko D. Petković, Paul Barry

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)803-816
Number of pages14
JournalIntegral Transforms and Special Functions
Volume23
Issue number11
DOIs
Publication statusPublished - Nov 2012

Keywords

  • Catalan numbers
  • Hankel transform
  • series reversion

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