Sobolev orthogonal polynomials in computing of Hankel determinants

Predrag M. Rajković, Paul Barry, Marko D. Petković

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we study closed form evaluation for some special Hankel determinants arising in combinatorial analysis, especially for the bidirectional number sequences. We show that such problems are directly connected with the theory of quasi-definite discrete Sobolev orthogonal polynomials. It opens a lot of procedural dilemmas which we will try to exceed. A few examples deal with Fibonacci numbers and power sequences will illustrate our considerations. We believe that our usage of Sobolev orthogonal polynomials in Hankel determinant computation is quite new.

Original languageEnglish
Pages (from-to)2417-2428
Number of pages12
JournalLinear Algebra and Its Applications
Volume437
Issue number10
DOIs
Publication statusPublished - 15 Nov 2012

Keywords

  • Hankel determinants
  • Orthogonal Polynomials
  • Recurrence relations
  • Sobolev space

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