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SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS

Year 2021, Volume: 3 Issue: 1, 15 - 19, 02.06.2021

Adem Şahin , Müzeyyen Demir

https://izlik.org/JA93GR93EG

Abstract

In this article, we give proofs of some properties provided by hyperbolic trigonometric functions defined in [4].

Keywords

Trigonometric functions, hyperbolic trigonometric functions, generalized Fibonacci and Lucas polynomials

References

  • Azman, H., k-Lucas Hiperbolik, Yarı-Hiperbolik Tribonacci ve Yarı-Hiperbolik Tribonacci-Lucas Fonksiy- onları.Ph. D. Dissertation, Gazi Üniversitesi. Ankara.
  • Falcon, S., Plaza, A., The k-Fibonacci hyperbolic functions. Chaos. Solitons and Fractals. 38(2008), 409- 420.
  • Guncan, A.N., Erbil, Y., The q-Fibonacci Hyperbolic Functions. Appl. Math. 8(2014), 81-88.
  • Li, H. ve MacHenry, T., 2013. The convolution ring of arithmetic functions and symmetric polynmials, Rocky Mount. Math.,(43),1-33
  • Rearick, D., Operators on algepras os aritmetic functions. Duke. Math. J. 35(1968), 761-766.
  • Stakhov, A., Rozin, B., On a new class of hyperbolic functions. Chaos. Solitons and Fractals. 23(2005), 379-389.
  • Stakhov, A., Rozin, B., The Golden Shofar. Chaos. Solitons and Fractals. 26(3)(2005), 677-684.
  • Stakhov, A., Rozin, B., The continuos functions for the Fibonacci and Lucas p-numbers. Chaos. Solitons and Fractals. 28(4)(2006), 1014-1025.
  • Stakov, A., Aranson, S., Hyperbolic Fibonacci and Lucas Functions, "Golden" Fibonacci Goniometry. Bodnar's Geometry and Hilbert's Fourth Problem. Appl. Math. 2(2011), 74-84

Year 2021, Volume: 3 Issue: 1, 15 - 19, 02.06.2021

Adem Şahin , Müzeyyen Demir

https://izlik.org/JA93GR93EG

Abstract

References

  • Azman, H., k-Lucas Hiperbolik, Yarı-Hiperbolik Tribonacci ve Yarı-Hiperbolik Tribonacci-Lucas Fonksiy- onları.Ph. D. Dissertation, Gazi Üniversitesi. Ankara.
  • Falcon, S., Plaza, A., The k-Fibonacci hyperbolic functions. Chaos. Solitons and Fractals. 38(2008), 409- 420.
  • Guncan, A.N., Erbil, Y., The q-Fibonacci Hyperbolic Functions. Appl. Math. 8(2014), 81-88.
  • Li, H. ve MacHenry, T., 2013. The convolution ring of arithmetic functions and symmetric polynmials, Rocky Mount. Math.,(43),1-33
  • Rearick, D., Operators on algepras os aritmetic functions. Duke. Math. J. 35(1968), 761-766.
  • Stakhov, A., Rozin, B., On a new class of hyperbolic functions. Chaos. Solitons and Fractals. 23(2005), 379-389.
  • Stakhov, A., Rozin, B., The Golden Shofar. Chaos. Solitons and Fractals. 26(3)(2005), 677-684.
  • Stakhov, A., Rozin, B., The continuos functions for the Fibonacci and Lucas p-numbers. Chaos. Solitons and Fractals. 28(4)(2006), 1014-1025.
  • Stakov, A., Aranson, S., Hyperbolic Fibonacci and Lucas Functions, "Golden" Fibonacci Goniometry. Bodnar's Geometry and Hilbert's Fourth Problem. Appl. Math. 2(2011), 74-84
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Adem Şahin

Müzeyyen Demir This is me

Acceptance Date April 5, 2021
Publication Date June 2, 2021
IZ https://izlik.org/JA93GR93EG
Published in Issue Year 2021 Volume: 3 Issue: 1

Cite

APA Şahin, A., & Demir, M. (2021). SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS. Ikonion Journal of Mathematics, 3(1), 15-19. https://izlik.org/JA93GR93EG
AMA 1.Şahin A, Demir M. SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS. ikjm. 2021;3(1):15-19. https://izlik.org/JA93GR93EG
Chicago Şahin, Adem, and Müzeyyen Demir. 2021. “SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS”. Ikonion Journal of Mathematics 3 (1): 15-19. https://izlik.org/JA93GR93EG.
EndNote Şahin A, Demir M (June 1, 2021) SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS. Ikonion Journal of Mathematics 3 1 15–19.
IEEE [1]A. Şahin and M. Demir, “SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS”, ikjm, vol. 3, no. 1, pp. 15–19, June 2021, [Online]. Available: https://izlik.org/JA93GR93EG
ISNAD Şahin, Adem - Demir, Müzeyyen. “SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS”. Ikonion Journal of Mathematics 3/1 (June 1, 2021): 15-19. https://izlik.org/JA93GR93EG.
JAMA 1.Şahin A, Demir M. SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS. ikjm. 2021;3:15–19.
MLA Şahin, Adem, and Müzeyyen Demir. “SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS”. Ikonion Journal of Mathematics, vol. 3, no. 1, June 2021, pp. 15-19, https://izlik.org/JA93GR93EG.
Vancouver 1.Adem Şahin, Müzeyyen Demir. SOME IDENTITIES FOR HYPERBOLIC TRIGONOMETRIC FUNCTIONS. ikjm [Internet]. 2021 Jun. 1;3(1):15-9. Available from: https://izlik.org/JA93GR93EG