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Journals / Konuralp Journal of Mathematics / 2026 / Volume: 13 Issue: 1

On a New Generalization of Bivariate Fibonacci Polynomials and Their Matrix Representations

Hayrullah Özimamoğlu(Nevşehir Hacı Bektaş Veli Üniversitesi)0000-0001-7844-1840
Pages
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Publication Date
2025-04-30
DOI
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AI Summary & Key Takeaways

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

By Riordan method, we give two new factorizations of the infinite Pascal matrix including the d-bivariate Fibonacci polynomials.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we introduce the concept of d-bivariate Fibonacci polynomials, which generalize the classical bivariate Fibonacci polynomials.
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Key Findings & Data:We obtain several fundamental properties for these new polynomials including the generating function, the Binet’s formula, combinatorial identities and summation formulas.
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Conclusion & Impact:By Riordan method, we give two new factorizations of the infinite Pascal matrix including the d-bivariate Fibonacci polynomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bivariate Fibonacci polynomials · d-bivariate Fibonacci polynomials · Pascal matrix

Abstract

In this study, we introduce the concept of d-bivariate Fibonacci polynomials, which generalize the classical bivariate Fibonacci polynomials. We obtain several fundamental properties for these new polynomials including the generating function, the Binet’s formula, combinatorial identities and summation formulas. Then, we define the infinite d-bivariate Fibonacci polynomials matrix, which is a Riordan matrix. By Riordan method, we give two new factorizations of the infinite Pascal matrix including the d-bivariate Fibonacci polynomials.

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Cite This Article

Özimamoğlu, H. (2025). On a New Generalization of Bivariate Fibonacci Polynomials and Their Matrix Representations. Konuralp Journal of Mathematics, Volume: 13 Issue: 1. https://ajindex.com/articles/1521482

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