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

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)

References

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