Special Identities of the Stakhov Hyperbolic Functions

Ahmet Daşdemir

doi:10.47000/tjmcs.1751182

Special Identities of the Stakhov Hyperbolic Functions

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.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Ahmet Daşdemir ^*
0000-0001-8352-2020
Türkiye

Publication Date

February 23, 2026

Submission Date

July 25, 2025

Acceptance Date

November 3, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1751182

IZ

https://izlik.org/JA37BX64SH

Cite

RIS / Bibtex

APA

Daşdemir, A. (2026). Special Identities of the Stakhov Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science, 18(1), 24-31. https://doi.org/10.47000/tjmcs.1751182

AMA

1.Daşdemir A. Special Identities of the Stakhov Hyperbolic Functions. TJMCS. 2026;18(1):24-31. doi:10.47000/tjmcs.1751182

Chicago

Daşdemir, Ahmet. 2026. “Special Identities of the Stakhov Hyperbolic Functions”. Turkish Journal of Mathematics and Computer Science 18 (1): 24-31. https://doi.org/10.47000/tjmcs.1751182.

EndNote

Daşdemir A (February 1, 2026) Special Identities of the Stakhov Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science 18 1 24–31.

IEEE

[1]A. Daşdemir, “Special Identities of the Stakhov Hyperbolic Functions”, TJMCS, vol. 18, no. 1, pp. 24–31, Feb. 2026, doi: 10.47000/tjmcs.1751182.

ISNAD

Daşdemir, Ahmet. “Special Identities of the Stakhov Hyperbolic Functions”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 24-31. https://doi.org/10.47000/tjmcs.1751182.

JAMA

1.Daşdemir A. Special Identities of the Stakhov Hyperbolic Functions. TJMCS. 2026;18:24–31.

MLA

Daşdemir, Ahmet. “Special Identities of the Stakhov Hyperbolic Functions”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 24-31, doi:10.47000/tjmcs.1751182.

Vancouver

1.Ahmet Daşdemir. Special Identities of the Stakhov Hyperbolic Functions. TJMCS. 2026 Feb. 1;18(1):24-31. doi:10.47000/tjmcs.1751182