On Bicomplex Jacobsthal Numbers





Recurrences, Generating functions, Fibonacci numbers, Idempotents


In this article, bicomplex Jacobsthal and bicomplex Jacobsthal-Lucas numbers are introduced and some properties related to them are investigated.


Download data is not yet available.


F. T. Aydin, On bicomplex Pell and Pell-Lucas numbers, Communications in Advanced Mathematical Sciences 1(2) (2018), 142 – 155, DOI: 10.33434/cams.439752.

F. T. Aydin and S. Yuce, A new approach to Jacobsthal quaternions, Filomat 31 (2017), 5567 – 5579, DOI: 10.2298/FIL1718567T.

F. Babadag, Dual bicomplex Fibonacci numbers with Fibonacci and Lucas numbers, Journal of Informatics and Mathematical Sciences 10(1-2) (2018), 161 – 172, DOI: 10.26713/jims.v10i1-2.575.

S. Falcon, On the k-Jacobsthal numbers, American Review of Mathematics and Statistics 2(1) (2014), 67 – 77, URL: http://armsnet.info/journals/arms/Vol_2_No_1_March_2014/8.pdf.

D. Dutta, S. Dey, S. Sarkar and S. K. Datta, A note on infinite product of bicomplex numbers, Journal of Fractional Calculus and Applications 12(1) (2021), 133 – 142, URL: http://math-frac.org/Journals/JFCA/Vol12(1)_Jan_2021/Vol12(1)_Papers/Volume12(1)_Paper12_Abstract.html.

S. Halici, On bicomplex Fibonacci numbers and their generalization, in: C. Flaut, S. Hošková-Mayerová and D. Flaut (eds.), Models and Theories in Social Systems. Studies in Systems, Decision and Control, Vol. 179 (2019), 509 – 524, Springer, Cham., DOI: 10.1007/978-3-030-00084-4_26.

S. Halici and S. Curuk, On some matrix representations of bicomplex numbers, Konuralp Journal of Mathematics 7(2) (2019), 449 – 455, URL: https://dergipark.org.tr/tr/download/articlefile/844622.

A. F. Horadam, Jacobsthal representation numbers, The Fibonacci Quarterly 26(1) (1996), 40 – 54, URL: https://www.fq.math.ca/Scanned/34-1/horadam2.pdf.

H. Kabadayi and Y. Yayli, Homothetic motions at E4 with bicomplex numbers, Advances in Applied Clifford Algebras 21(3) (2011), 541 – 546, DOI: 10.1007/s00006-010-0266-0.

N. Kilic, On k-Jacobsthal and k-Jacobsthal-Lucas octonions, JP Journal of Algebra, Number Theory and Applications 41(1) (2019), 1 – 17, DOI: 10.17654/NT041010001.

N. Kilic, On split k-Jacobsthal and k-Jacobsthal-Lucas quaternions, Ars Combinatoria 142 (2019), 129 – 139, URL: http://www.combinatoire.ca/ArsCombinatoria/Vol142.html.

M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions, CUBO A Mathematical Journal 14(2) (2012), 61 – 80, URL: https://scielo.conicyt.cl/pdf/cubo/v14n2/art04.pdf.

M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis of Bicomplex Numbers, Birkhuser (2015), URL: https://link.springer.com/book/10.1007/978-3-319-24868-4.

S. K. Nurkan and I. A. Guven, A note on bicomplex fibonacci and lucas numbers, International Journal of Pure and Applied Mathematics 120(3) (2018), 365 – 377, DOI: 10.12732/ijpam.v120i3.7.

Y. Soykan and E. Tasdemir, On bicomplex generalized Tetranacci quaternions, Notes on Number Theory and Discrete Mathematics 26(3) (2020), 163 – 175, DOI: 10.7546/nntdm.2020.26.3.163-175.

D. Tasci, On k-Jacobsthal and k-Jacobsthal Lucas quaternions, Journal of Science and Arts 3(40) (2017), 469 – 476, URL: http://www.josa.ro/docs/josa_2017_3/a_10_Tasci_469.pdf.

M. A. Wagh, Introduction of Bicomplex Numbers, Department of Mathematics, Deendayal Upadhyaya College, University of Delhi, India (2018), https://www.researchgate.net/profile/Mamta-Wagh/publication/327883801_INTRODUCTION_TO_BICOMPLEX_NUMBERS/links/5bab4456299bf13e604ca693/INTRODUCTION-TO-BICOMPLEX-NUMBERS.pdf.

S. Yasarsoy, M. Acikgoz and U. Duran, A study on the k-Jacobsthal and k-Jacobsthal Lucas quaternions and octonions, Journal of Analysis & Number Theory 6(2) (2018), 39 – 45, DOI: 10.18576/jant/060201.




How to Cite

Kilic, N. (2021). On Bicomplex Jacobsthal Numbers. Communications in Mathematics and Applications, 12(4), 969–976. https://doi.org/10.26713/cma.v12i4.1529



Research Article