TY - JOUR
T1 - Determinants containing powers of polynomial sequences
AU - Leung, H. H.
N1 - Funding Information:
The author was supported in part by the UAEU Startup Grant 2016, Grant No. G00002235.
Funding Information:
The author expresses his gratitude to the Mahidol University International College (MUIC) at Bangkok, Thailand for their hospitality in hosting me in May 2018. The author is grateful to Thotsaporn Thanatipanonda for generously sharing his ideas on the topic. The author is supported by Startup Grant 2016 (G00002235) which is funded by United Arab Emirates University.
Publisher Copyright:
© 2018 Miskolc University Press
PY - 2018
Y1 - 2018
N2 - 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.
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.
KW - Chebyshev polynomial
KW - determinant identity
KW - Fibonacci polynomial
KW - Lucas polynomial
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U2 - 10.18514/MMN.2018.2682
DO - 10.18514/MMN.2018.2682
M3 - Article
AN - SCOPUS:85110574960
VL - 19
SP - 1019
EP - 1033
JO - Miskolc Mathematical Notes
JF - Miskolc Mathematical Notes
SN - 1787-2405
IS - 2
ER -