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


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Kilic E., ÖMÜR N., KOPARAL S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.2, pp.684-694, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.473495
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.684-694
  • Keywords: generalized Filbert matrix, q-analogues, LU-decomposition, Zeilberger's algorithm, computer algebra system (CAS), GENERALIZED FIBONACCI MATRIX, DETERMINANT

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.