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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 75 Issue: 3

Theory and Applications of the Conditional Type Hyperbolic Functions

Cahit Köme(NEVSEHIR HACI BEKTAS VELI UNIVERSITY)0000-0002-6488-9035
Zeynep Demirel(NEVSEHIR HACI BEKTAS VELI UNIVERSITY)0009-0007-9699-8133
Sayfa
—
Yayın Tarihi
2026-09-26
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we present numerical and graphical illustrations to support the theoretical findings.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we introduce conditional and symmetric conditional hyperbolic $\textit{sine}$ and $\textit{cosine}$ functions by replacing a discrete variable with a continuous one and employing conditionally defined sequences.
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Temel Bulgular & Veri:We establish fundamental relations between these functions and derive their generating and exponential generating functions, recurrence relations, sums and differences, double arguments, derivatives, De Moivre-type identities, and several key properties.
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Sonuç & Katkı:Finally, we present numerical and graphical illustrations to support the theoretical findings.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Golden ratio · conditional sequence · hyperbolic function

Abstract

In this paper, we introduce conditional and symmetric conditional hyperbolic $\textit{sine}$ and $\textit{cosine}$ functions by replacing a discrete variable with a continuous one and employing conditionally defined sequences. We establish fundamental relations between these functions and derive their generating and exponential generating functions, recurrence relations, sums and differences, double arguments, derivatives, De Moivre-type identities, and several key properties. Furthermore, we construct a quasi-sine conditional hyperbolic function by selecting an appropriate trigonometric function. Using these results, we develop three-dimensional conditional spiral and shofar structures. Finally, we present numerical and graphical illustrations to support the theoretical findings.

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Bu Makaleye Atıf Yap

Köme, C., Demirel, Z. (2026). Theory and Applications of the Conditional Type Hyperbolic Functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 75 Issue: 3. https://doi.org/10.31801/cfsuasmas.1622874

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