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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2020 / Cilt: 13 - Sayı: Özel Sayı - 1

Catalan Transform of The 𝒌 −Lucas Numbers

Engin ÖZKAN
Merve TAŞTAN
Olcay GÜNGÖR
Pages
145–149
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

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

Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the 𝐶𝐿𝑘,𝑛 description of Catalan transformation of 𝑘 −Lucas 𝐿𝑘,𝑛 sequences was given.
📊
Key Findings & Data:And also, 𝐶𝐿𝑘,𝑛 transformation was written as the multiplying of Catalan matris C which is the lower triangular matris, and the 𝐿𝑘 matris of 𝑛 𝑥 1 type.
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Conclusion & Impact:Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, the 𝐶𝐿𝑘,𝑛 description of Catalan transformation of 𝑘 −Lucas 𝐿𝑘,𝑛 sequences was given. The 𝐶𝐿𝑘,𝑛 generating function of Catalan transformation of 𝑘 −Lucas 𝐿𝑘,𝑛 sequences was obtained. And also, 𝐶𝐿𝑘,𝑛 transformation was written as the multiplying of Catalan matris C which is the lower triangular matris, and the 𝐿𝑘 matris of 𝑛 𝑥 1 type. Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.

Özet

Bu çalışmada, 𝑘–Lucas dizisinin 𝐿𝑘,𝑛 Catalan dönüşümünün 𝐶𝐿𝑘,𝑛 tanımı verildi. 𝑘–Lucas dizisinin 𝐿𝑘,𝑛 Catalan dönüşümünün 𝐶𝐿𝑘,𝑛 geren fonksiyonu elde edildi. Ayrıca, 𝐶𝐿𝑘,𝑛 dönüşümü, alt üçgen matris olan Catalan matrisi 𝐶 ile 𝑛 × 1 tipindeki 𝐿𝑘 matrisinin çarpımı olarak yazıldı. Hankel fonksiyonu kullanılarak 𝐶𝐿𝑘,𝑛 ler ile oluşturulan matrislerin determinantları hesaplandı.

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Cite This Article

ÖZKAN, E., TAŞTAN, M., GÜNGÖR, O. (2022). Catalan Transform of The 𝒌 −Lucas Numbers. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 - Sayı: Özel Sayı - 1, 145–149. https://ajindex.com/articles/505435

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