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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 2

On unrestricted dual-generalized complex Horadam numbers

Nacima Rosa Ait-amrane(Medea University)0000-0002-0241-996X
Elif Tan(ANKARA ÜNİVERSİTESİ)0000-0002-8381-8750
Pages
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Publication Date
2024-06-21
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AI Summary & Key Takeaways

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

Additionally, a comprehensive bilinear index-reduction formula is derived, which encompasses Vajda’s, Catalan’s, Cassini’s, D’Ocagne’s, and Halton’s identities as specific cases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This research introduces a novel category of dual-generalized complex numbers, with components represented by unrestricted Horadam numbers.
📊
Key Findings & Data:We present various recurrence relations, summation formulas, the Binet formula, and the generating function associated with these numbers.
💡
Conclusion & Impact:Additionally, a comprehensive bilinear index-reduction formula is derived, which encompasses Vajda’s, Catalan’s, Cassini’s, D’Ocagne’s, and Halton’s identities as specific cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hypercomplex numbers · dual generalized complex numbers · Horadam numbers

Abstract

This research introduces a novel category of dual-generalized complex numbers, with components represented by unrestricted Horadam numbers. We present various recurrence relations, summation formulas, the Binet formula, and the generating function associated with these numbers. Additionally, a comprehensive bilinear index-reduction formula is derived, which encompasses Vajda’s, Catalan’s, Cassini’s, D’Ocagne’s, and Halton’s identities as specific cases.

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Cite This Article

Ait-amrane, N. R., Tan, E. (2024). On unrestricted dual-generalized complex Horadam numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 2. https://doi.org/10.31801/cfsuasmas.1406328

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