Determinants containing powers of polynomial sequences

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Abstract

We derive identities for the determinants of matrices whose entries are (rising) powers of (products of) polynomials that satisfy a recurrence relation. In particular, these results cover the cases for Fibonacci polynomials, Lucas polynomials and certain orthogonal polynomials. These identities naturally generalize the determinant identities obtained by Alfred, Carlitz, Prodinger, Tangboonduangjit and Thanatipanonda.

Original languageEnglish
Pages (from-to)1019-1033
Number of pages15
JournalMiskolc Mathematical Notes
Volume19
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • Chebyshev polynomial
  • determinant identity
  • Fibonacci polynomial
  • Lucas polynomial

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Numerical Analysis
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

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