TY  - JOUR
T1  - New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries
AU  - Koparal, Sibel
AU  - Kılıç, Emrah
AU  - Ömür, Neşe
PY  - 2020
DA  - April
DO  - 10.15672/hujms.473495
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 684
EP  - 694
VL  - 49
IS  - 2
LA  - en
AB  - In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulae for their $LU$-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.
KW  - Generalized Filbert matrix
KW  - q-analogues
KW  - LU-decomposition
KW  - Zeilberger’s algorithm
KW  - Computer algebra system (CAS)
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UR  - https://doi.org/10.15672/hujms.473495
L1  - https://dergipark.org.tr/en/download/article-file/755689
ER  -