New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries

Authors : Emrah KILIÇ, Neşe ÖMÜR, Sibel KOPARAL

Pages : 684-694

Doi:10.15672/hujms.473495

View : 14 | Download : 4

Publication Date : 2020-04-02

Article Type : Research Paper

Abstract :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.
Keywords : Generalized Filbert matrix, q analogues, LU decomposition, Zeilbergers algorithm, Computer algebra system CAS,