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 (SCI-Expanded)

• 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 (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
• Page Numbers: pp.684-694
• Kocaeli University Affiliated: Yes

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.