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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

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

Emrah Kılıç
Neşe Ömür
Sibel Koparal
Pages
684–694
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data:We shall derive explicit formulae for their $LU$-decompositions and inverses.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

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Cite This Article

Kılıç, E., Ömür, N., Koparal, S. (2022). New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 684–694. https://ajindex.com/articles/529594

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