TY  - JOUR
T1  - ON THE LAGRANGE INTERPOLATIONS OF THE JACOBSTHAL AND JACOBSTHAL-LUCAS SEQUENCES
AU  - Dişkaya, Orhan
PY  - 2024
DA  - December
Y2  - 2024
DO  - 10.33773/jum.1518403
JF  - Journal of Universal Mathematics
JO  - JUM
PB  - Gökhan ÇUVALCIOĞLU
WT  - DergiPark
SN  - 2618-5660
SP  - 128
EP  - 137
VL  - 7
IS  - To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI"
LA  - en
AB  - This study explores the formation of polynomials of at most degree $n$ using the first $n+1$ terms of the Jacobsthal and Jacobsthal-Lucas sequences through Lagrange interpolation. The paper provides a detailed examination of the recurrence relations and various identities associated with the Jacobsthal and Jacobsthal-Lucas Lagrange Interpolation Polynomials.
KW  - Fibonacci numbers
KW  - Lucas numbers
KW  - Jacobsthal numbers
KW  - Lagrange interpolations
KW  - Binet formula
CR  - M. Asci, E. GUrel, Gaussian Jacobsthal and Gaussian Jacobsthal Lucas Numbers, Ars Combinatoria,	Vol.5, No.111, pp.53-62 (2013).
CR  - P. Catarino, P. Vasco, H. Campos, A. P. Aires, A. Borges,  New families of Jacobsthal and Jacobsthal-Lucas numbers, Algebra and Discrete Mathematics, vol.20, No.1, (2015).
CR  - G. Cerda-Morales,  On bicomplex third-order Jacobsthal numbers, Complex Variables and Elliptic Equations, Vol.68, No.1, pp.44-56 (2023).
CR  - C. K. Cook, M. R. Bacon,   Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations. In Annales mathematicae et informaticae, pp. 27-39 (2013).
CR  - C. B. Cimen, A. Ipek, On jacobsthal and jacobsthal–lucas octonions, Mediterranean Journal of Mathematics, Vol.14, pp.1-13 (2017).
CR  - A. DaSdemir, On the Jacobsthal numbers by matrix method. SUleyman Demirel University Faculty of Arts and Science Journal of Science, vol.7, No.1, pp.69-76 (2012).
CR  - O. Deveci and G. Artun, On the adjacency-Jacobsthal numbers, Communications in Algebra, vol.47, No.11, pp.4520-4532 (2019).
CR  - C. M. Dikmen,   Hyperbolic jacobsthal numbers, Asian Research Journal of Mathematics, Vol.15, No.4, pp.1-9 (2019).
		
O. Diskaya, H. Menken, On the Jacobsthal and Jacobsthal-Lucas Subscripts, J. Algebra Comput. Appl, Vol.8, pp.1-6 (2019).
CR  - V. E. Hoggatt Jr, M. Bicknell-Johnson,  Convolution arrays for Jacobsthal and Fibonacci polynomials, The Fibonacci Quarterly, Vol.16, No.5, pp.385-402 (1978).
CR  - A. F. Horadam, Jacobsthal representation numbers, significance, Vol.2, pp.2-8 (1996).
CR  - C. KızılateS,  On the Quadra Lucas-Jacobsthal Numbers, Karaelmas Science  Engineering Journal/Karaelmas Fen ve MUhendislik Dergisi, Vol.7, No.2, (2017).
CR  - J. Kiusalaas,  Numerical methods in engineering with Python. Cambridge university press, (2010).	
			
		
E. Ozkan, B. Kuloglu, On a Jacobsthal-like sequence associated with k-Jacobsthal-Lucas sequence. Journal of Contemporary Applied Mathematics, Vol.10, No.2, pp. 3-13, (2020).
CR  - E. Ozkan,  M. Uysal, B. Kuloglu, Catalan transform of the incomplete Jacobsthal numbers and incomplete generalized Jacobsthal polynomials. Asian-European Journal of Mathematics, Vol.15, No.06, pp. 2250119, (2022).
CR  - B. Kuloğlu, E. Ozkan, Applications of Jacobsthal and Jacobsthal-Lucas Numbers in Coding Theory, pp. 54-64, (2023).
CR  - M. S. U. Mufid, T. Asfihani, L. Hanafi,  On the Lagrange interpolation of Fibonacci sequence, (IJCSAM) International Journal of Computing Science and Applied Mathematics, Vol.2, No.3, pp.38-40 (2016).
CR  - E. Ozkan, M. Uysal, On quaternions with higher order Jacobsthal numbers components, Gazi University Journal of Science, pp.1-1  (2023).
CR  - E. E. Polatlı, Y. Soykan  On generalized third-order Jacobsthal numbers, Asian Research Journal of Mathematics, Vol.17, No.2, pp.1-19, (2021).
CR  - E. SUli, D. F. Mayers, An introduction to numerical analysis, Cambridge university press, (2003).
CR  - N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, (A001045). 	https://oeis.org/A001045, (1973).
CR  - N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, (A014551). 	https://oeis.org/A014551, (1973).
CR  - S. Uygun,  The (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas sequences, Applied Mathematical Sciences, Vol.70, No.9, pp.3467-3476 (2015).
UR  - https://doi.org/10.33773/jum.1518403
L1  - https://dergipark.org.tr/tr/download/article-file/4080069
ER  -