Abstract
Jacobsthal numbers satisfy a second order homogeneous recurrence relation $J_{n}=J_{n-1}+2J_{n-2}$ where $J_{n}$ denotes the $n^{th}$ Jacobsthal number. In this paper, the Jacobsthal sine, cosine, tangent and cotangent are defined, and some identities of Jacobsthal trigonometric functions are provided.
Full text article
References
D. Kalman and R. Mena, “The fibonacci numbers-exposed,” The Mathematical Magazine, vol. 76, no. 3, pp. 167–181, 2003. https://doi.org/10.2307/3219318.
T. Koshy, Fibonacci and Lucas numbers with applications. New York: Wiley-Interscience, 2001. https://doi.org/10.1002/9781118033067.
A. F. Horadam, “Jacobsthal representation numbers,” The Fibonacci Quarterly, vol. 34, pp. 40–54, 1996. https://doi.org/10.1080/00150517.1996.12429096.
R. M. Smith, “Introduction to analytic fibonometry,” Alabama Journal of Mathematics, vol. 25, no. 2, pp. 27–36, 2001.
V. Srimuk and A. Pakapongpun, “Identities of k-fibonometric functions,” Burapha Science Journal, vol. 25, no. 3, pp. 880–891, 2020.
W. M. Abd-Elhameed, O. M. Alqubori, and A. K. Amin, “New results for certain jacobsthal-type polynomials,” Mathematics, vol. 13, no. 5, p. 715, 2025. https://doi.org/10.3390/math13050715.
I. Ye¸silyurt and N. De˘girmen, “Non-newtonian jacobsthal and jacobsthal-lucas numbers: A new look,” Filomat, vol. 39, no. 4, pp. 1093–1109, 2025. https://doi.org/10.2298/FIL2504093Y
Authors
Copyright (c) 2025 Journal of the Indonesian Mathematical Society
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Article Details
