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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 1

Special Identities of the Stakhov Hyperbolic Functions

Ahmet Daşdemir(kastamonu üniversitesi)0000-0001-8352-2020
Pages
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Publication Date
2026-02-23
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AI Summary & Key Takeaways

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

The unified framework bridges recurrence sequences and hyperbolic function theory and demonstrates applications in differential geometry.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper establishes fundamental algebraic identities for Stakhov hyperbolic functions, a recent generalization of hyperbolic functions based on recurrence sequences with functional parameters.
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Key Findings & Data:The matrix methodology thus generates further identities—including Honsberger-type decompositions and shift formulas—thereby unifying discrete recurrences with continuous symmetries.
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Conclusion & Impact:The unified framework bridges recurrence sequences and hyperbolic function theory and demonstrates applications in differential geometry.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Stakhov hyperbolic function · Gelin-Cesàro identity · Honsberger formula

Abstract

This paper establishes fundamental algebraic identities for Stakhov hyperbolic functions, a recent generalization of hyperbolic functions based on recurrence sequences with functional parameters. We derive Vajda-type additivity relations, d’Ocagne’s formulas, Catalan and Cassini-type multiplicative laws, Gelin–Cesàro–type identities, and generating functions through Binet’s formulas, and introduce a novel platinum matrix framework. The matrix methodology thus generates further identities—including Honsberger-type decompositions and shift formulas—thereby unifying discrete recurrences with continuous symmetries. Special cases recover classical identities for hyperbolic Fibonacci functions, and new results emerge for Pell, Jacobsthal, and Fermat-type generalizations. The unified framework bridges recurrence sequences and hyperbolic function theory and demonstrates applications in differential geometry.

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Cite This Article

Daşdemir, A. (2026). Special Identities of the Stakhov Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 1. https://doi.org/10.47000/tjmcs.1751182

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