Two-parameter generalization of bihyperbolic Jacobsthal numbers
DOI:
https://doi.org/10.22199/issn.0717-6279-4071Keywords:
Jacobsthal numbers, bihyperbolic numbers, bihyperbolic Jacobsthal numbers, recurrence relations, generating functionsAbstract
In this paper we define a two-parameter generalization of bihyperbolic Jacobsthal numbers. We give Binet formula, the generating functions and some identities for these numbers.
References
M. Bilgin and S. Ersoy, “Algebraic Properties of Bihyperbolic Numbers”, Advances in Applied Clifford Algebras, vol. 30 no. 13, 2020. https://doi.org/10.1007/s00006-019-1036-2
D. Bród, “On a two-parameter generalization of Jacobsthal numbers and its graph interpretation”, Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica (Online), vol. 72, no. 2, pp. 21-28, 2018. http://dx.doi.org/10.17951/a.2018.72.2.21
D. Bród and A. Szynal-Liana, “On a new generalization of Jacobsthal quaternions and several identities involving these numbers”, Commentationes Mathematicae, vol. 1-2, no. 59, pp. 33-45, 2019. http://dx.doi.org/10.14708/cm.v59i1-2.6492
D. Bród and A. Szynal-Liana, “On J(r, n)-Jacobsthal Quaternions”, Pure and Applied Mathematics Quarterly, vol. 14 no. 3-4, pp. 579-590, 2018. https://dx.doi.org/10.4310/PAMQ.2018.v14.n3.a7
F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti, and P. Zampetti, The mathematics of Minkowski space-time with an introduction to commutative hypercomplex numbers. Basel: Birkhäuser, 2008.
A. Dasdemir, “The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence”, Hittite Journal of Science and Engineering, vol. 3 no. 2, pp. 99-104, 2016. https://doi.org/10.17350/HJSE19030000038
S. Falcon, “On the k-Jacobsthal Numbers”, American Review of Mathematics and Statistics, vol. 2 No. 1, pp. 67-77, 2014.
D. Jhala, K. Sisodiya and G. P. S. Rathore, “On Some Identities for k-Jacobsthal Numbers”, International Journal of Mathematical Analysis, vol. 7, no. 12, pp. 551-556, 2013. http://dx.doi.org/10.12988/ijma.2013.13052
S. Olariu, Complex Numbers in n dimensions. Amsterdam: North-Holland, 2002.
A. A. Pogorui, R. M. Rodríguez-Dagnino and R. D. Rodríguez-Said, “On the set of zeros of bihyperbolic polynomials”, Complex Variables and Elliptic Equations, vol. 53, no. 7, 2008. https://doi.org/10.1080/17476930801973014
D. Rochon and M. Shapiro, “On algebraic properties of bicomplex and hyperbolic numbers”, Analele Universităt¸ii Oradea, Fascicola Matematica, vol. 11, pp. 71-110, 2004.
G. Sobczyk, “The Hyperbolic Number Plane”, The College Mathematics Journal, vol. 26, no. 4, 1995. https://doi.org/10.1080/07468342.1995.11973712
A. Szynal-Liana, “The Horadam Hybrid Numbers”, Discussiones Mathematicae. General Algebra and Applications (Online), vol. 38, pp. 91-98, 2018. http://dx.doi.org/10.7151/dmgaa.1287
A. Szynal-Liana and I. Włoch, “A note on Jacobsthal quaternions”, Advances in Applied Clifford Algebras, vol. 26, pp. 441-447, 2016. https://doi.org/10.1007/s00006-015-0622-1
A. Szynal-Liana and I. WÃloch, Hypercomplex numbers of the Fibonacci type. Rzeszów: Oficyna Wydawnicza Politechniki Rzeszowskiej, 2019.
A. Szynal-Liana and I. WÃloch, “On Jacobsthal and Jacobsthal-Lucas hybrid numbers”, Annales Mathematicae Silesianae, vol. 33, pp. 276-283, 2019. https://doi.org/10.2478/amsil-2018-0009
S. Uygun, “The (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas Sequences”, Applied Mathematical Sciences, vol. 9, no. 70, pp. 3467-3476, 2015. http://dx.doi.org/10.12988/ams.2015.52166
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