Determinants containing powers of polynomial sequences

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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
Issue number2
Publication statusPublished - 2018


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

ASJC Scopus subject areas

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


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