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Journals / Konuralp Journal of Mathematics / 2025 / Volume: 13 Issue: 2

On the Francois Polynomials and Hybrinomials

Efruz Özlem Mersin(AKSARAY ÜNİVERSİTESİ)0000-0001-6260-9063
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Publication Date
2025-10-31
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Moreover, we derive the Catalan, Cassini, and d'Ocagne identities for these polynomials and hybrinomials.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper introduces the Francois polynomials and Francois hybrinomials, which are generalized forms of the Francois numbers and Francois hybrid numbers, respectively.
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Key Findings & Data:We explore their recurrence relations, summation formulas, generating functions, and Binet-type formulas.
💡
Conclusion & Impact:Moreover, we derive the Catalan, Cassini, and d'Ocagne identities for these polynomials and hybrinomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Binet formula · Catalan identity · d'Ocagne identity

Abstract

This paper introduces the Francois polynomials and Francois hybrinomials, which are generalized forms of the Francois numbers and Francois hybrid numbers, respectively. We explore their recurrence relations, summation formulas, generating functions, and Binet-type formulas. Moreover, we derive the Catalan, Cassini, and d'Ocagne identities for these polynomials and hybrinomials.

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Cite This Article

Mersin, E. Ö. (2025). On the Francois Polynomials and Hybrinomials. Konuralp Journal of Mathematics, Volume: 13 Issue: 2. https://ajindex.com/articles/1521449

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