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 language | English |
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Pages (from-to) | 1019-1033 |
Number of pages | 15 |
Journal | Miskolc Mathematical Notes |
Volume | 19 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- 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