Determinants containing powers of polynomial sequences

H. H. Leung

doi:10.18514/MMN.2018.2682

Determinants containing powers of polynomial sequences

H. H. Leung

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	1019-1033
Number of pages	15
Journal	Miskolc Mathematical Notes
Volume	19
Issue number	2
DOIs	https://doi.org/10.18514/MMN.2018.2682
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

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10.18514/MMN.2018.2682

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AB - 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.

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KW - Fibonacci polynomial

KW - Lucas polynomial

KW - determinant identity

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Determinants containing powers of polynomial sequences

Abstract

Keywords

ASJC Scopus subject areas

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