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

Year 2020, Volume: 49 Issue: 2, 684 - 694, 02.04.2020

Emrah Kılıç Neşe Ömür Sibel Koparal

https://doi.org/10.15672/hujms.473495

Cited By: 1

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, Zeilberger’s algorithm, Computer algebra system (CAS)

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