Properties of Gaussian Generalized Leonardo Numbers

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Karaelmas Fen ve Mühendislik Dergisi
Cilt: 15 Sayı: 1
Properties of Gaussian Generalized Leonardo Numbers

Properties of Gaussian Generalized Leonardo Numbers

Authors : Can Murat Dikmen

Pages : 134-145

Doi:10.7212/karaelmasfen.1578154

View : 76 | Download : 47

Publication Date : 2025-04-22

Article Type : Research Paper

Abstract :In this research, we introduce and thoroughly examine Gaussian generalized Leonardo numbers, focusing on three distinct cases: Gaussian modified Leonardo numbers, Gaussian Leonardo‐Lucas numbers, and Gaussian Leonardo numbers. Our aim is to offer a comprehensive understanding of the behaviour and properties of these sequences. To this end, we perform a detailed analysis, deriving various identities and matrices associated with these sequences. We also explore key mathematical tools such as recurrence relations, Binet’s formulas, generating functions, Simpson’s formula, Honsberger’s identity, and several summation formulas. This multifaceted approach provides valuable insights into the structure and behaviour of these Gaussian-based sequences. The results we present not only extend existing knowledge but also open the door for future studies that could explore further generalizations and applications of Gaussian generalized Leonardo numbers.
Keywords : Gaussian genelleştirilmiş Leonardo sayıları, Gaussian Leonardo-Lucas sayıları, Gaussian modifiye Leonardo sayıları, Gaussian Leonardo sayıları

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