The Quasi-Hyperbolic Tribonacci and Quasi-Hyperbolic Tribonacci-Lucas Functions

Dursun Taşçı, Huriye Azman


In the present paper, we studied an extension of the classical hyperbolic functions. We wrote a new relation that is equal to the Binet formula of the Tribonacci-Lucas numbers. We defined the quasi-hyperbolic Tribonacci and quasi-hyperbolic Tribonacci-Lucas functions. Finally, we investigated the recurrence and hyperbolic properties of these new hyperbolic functions.


Tribonacci Numbers, Hyperbolic Functions, Quasi-Hyperbolic Functions

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W.R. Spickerman, Binets formula for the tribonacci sequence, Fibonacci Quarterly 20(2) (1982), 118-121.

A. Stakhov and I. Tkachenko, Hyperbolic fibonacci trigonometry, Rep. Ukr. Acad. Sci. 7(1993), 9-14.

Catalani M.Identities for Tribonacci-related sequences. arXiv:math/0209179v1 [math.CO], 15 Sep 2002.

T.D. Noe and J.V. Post, Primes in Fibonacci $n$-step and Lucas $n$-step sequences, J. of Integer Sequences 8 (2005), Article 05.4.4.

A. Stakhov and B. Rozin, On a new class of hyperbolic functions, Chaos, Solitons & Fractals 23(2) (2005), 379-389.

A. Stakhov, The generalized principle of the golden section and its applications in mathematics, science and engineering, Chaos, Solitons & Fractals 26(2) (2005), 263-289.

A. Stakhov and B. Rozin, The Golden Shofar, Chaos, Solitons & Fractals 26(3) (2005), 677-684.

A. Stakhov and B. Rozin, Theory of Binet formulas for Fibonacci and Lucas $p$-numbers, Chaos, Solitons & Fractals 27(5) (2005), 1163-1177.

A. Stakhov and B. Rozin, The continuous functions for the Fibonacci and Lucas $p$-numbers, Chaos, Solitons & Fractals 28(4) (2006), 1014-1125.

A.P. Stakhov, Gazale formulas, a new class of the hyperbolic Fibonacci and Lucas functions and the improved method of the "golden" cryptography, Academy of Trinitarism, Moscow: 77-6567, publication 14098, 21.12.2006.

A. Stakhov and B. Rozin, The "golden" hyperbolic models of Universe, Chaos, Solitons & Fractals 34(2)(2007), 159-171.

S. Falcon and A. Plaza, The $k$-Fibonacci hyperbolic functions, Chaos, Solitons & Fractals 38(2) (2008), 409-420.

E.G. Kocer, N. Tuglu and A. Stakhov, Hyperbolic functions with second order recurrence sequences, Ars Comb., 01/2008; 88.



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