HYPER-LEONARDO HYBRINOMIALS
Yıl 2023,
Cilt: 11 Sayı: 1, 91 - 103, 28.02.2023
Efruz Özlem Mersin
,
Mustafa Bahşi
Öz
The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.
The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.
The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.
Kaynakça
- [1] Falcón S, Plaza Á. On the Fibonacci k-numbers. Chaos, Solitons and Fractals 2007; 32 (5): 1615-1624.
- [2] Yazlik Y, Köme C, Mathusudanan V. A new generalization of Fibonacci and Lucas p-numbers. Journal of Computational Analysis and Applications 2018; 25 (4): 667-669.
- [3] Bernstein M, Sloane NJA. Some canonical sequences of integers. Linear Algebra and its Applications 1995; 226-228: 57-72. https://doi.org/10.1016/0024-3795(94)00245-9
- [4] Betten D. Kalahari and the sequence "Sloane No.377". Annals of Discrete Mathematics 1988; 37: 51-58. https://doi.org/10.1016/S01675060(08)70224-3
- [5] Cameron BJ. Some sequences of integers. Discrete Mathematics 1989; 75 (1-3): 89-102. https://doi.org/10.1016/0012-365X(89)90081-2
- [6] Koshy T. Fibonacci and Lucas numbers with applications. Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs and Tracts, New York: Wiley 2001.
- [7] Catarino PM, Borges A. On Leonardo numbers. Acta Mathematica Universitatis Comenianae 2020; 89 (1): 75-86.
- [8] Alp Y., Koçer GE. Hybrid Leonardo numbers. Chaos, Solitons and Fractals 2021;150: 111128. https://doi.org/10.1016/j.chaos.2021.111128
- [9] Soykan Y. Generalized Leonardo number. Journal of Progressive Research in Mathematics 2021; 18 (4): 58-84.
- [10] Soykan Y. Special cases of generalized Leonardo numbers: modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo numbers. Earthline Journal of Mathematical Sciences 2023; 11(2): 317-342.
- [11] Mersin EÖ, Bahşi M. Hyper-Leonardo numbers. Conference Proceedings of Science and Technology 2022; 5 (1): 14-20.
- [12] Shannon A.G. A note on generalized Leonardo numbers. Notes on Number Theory and Discrete Mathematics 2019; 25 (3): 97-101.
- [13] Kürüz F, Dağdeviren A. Catarino P. On Leonardo Pisano Hybrinomials. Mathematics 2021; 9 (22): 2923. https://doi.org/10.3390/math9222923
- [14] Mersin EÖ. Hyper-Leonardo polynomials. 9th International Congress on Fundamental and Applied Sciences (ICFAS2022) Proceeding book, icfas2022.intsa.org, ISBN 978-605-67052-7-4
- [15] Özdemir M. Introduction to hybrid numbers. Advances in Applied Clifford Algebras 2018; 28 (1): 1-32.
- [16] Szynal-Liana A. Wloch I. The Fibonacci hybrid numbers. Utilitas Mathematica 2019; 110.
- [17] Szynal-Liana A, Wloch I. Introduction to Fibonacci and Lucas hybrinomials. Complex Variables and Elliptic Equations 2020; 65(10): 1736-1747.
- [18] Szynal-Liana A, Wloch I. On Jacopsthal and Jacopsthal-Lucas hybrid numbers. Annales Mathematicae Silesianae 2019; 33: 276-283. https://doi.org/10.2478/amsil-2018-0009
- [19] Szynal-Liana A. The Horadam hybrid numbers. Discussiones Mathematicae General Algebra and Applications 2018; 38(1): 91-98.
- [20] Kızılateş C. A note on Horadam hybrinomials. Fundamental Journal of mathematics and Applications 2022; 5 (1): 1-9. https://doi.org/10.33401/fujma.993546
- [21] Öztürk İ, Özdemir M. Similarity of hybrid numbers. Mathematical Methods in Applied Sciences. 2020; 43(15): 8867-8881. https://doi.org/10.1002/mma.6580
- [22] Yağmur T. A note on generalized hybrid tribonacci numbers. Discussiones Mathematicae General Algebra and Applications 2020; 40:187-199.
[23] Dos Santos Mangueira MC, Vieira RPM, Alves FRV, Catarino PMMC. The hybrid numbers of Padovan and some identities. Annales Mathematicae Silesianae 2020; 34 (2): 256-267. https://doi.org/10.2478/amsil-2020-0019
- [24] Kızılateş C, A new generalization of Fibonacci hybrid and Lucas hybrid numbers. Chaos, Solitons and Fractals 2020; 130: 109449. https://doi.org/10.1016/j.chaos.2019.109449
- [25] Kızılateş C, Kone T. On higher order Fibonacci hyper complex numbers. Chaos, Solitons and Fractals 2021; 148; 111044. https://doi.org/10.1016/j.chaos.2021.111044
[26] Polatlı E. A note on ratios of Fibonacci hybrid and Lucas hybrid numbers. Notes on Number Theory and Discrete Mathematics 2021; 27 (3): 73-78.
- [27] Kızılateş C, Kone T. On special spacelike hybrid numbers with Fibonacci divisor number components. Indian Journal of Pure and Apllied Mathematics 2022;1-9.
- [28] Alp Y, Koçer GE. Hybrid Leonardo numbers. Chaos, Solitons and Fractals 2021; 150: 111128. https://doi.org/10.1016/j.chaos.2021.111128
- [29] Dağdeviren A, Kürüz F. On The Horadam Hybrid Quaternions. arXiv preprint 2020; arXiv:2012.08277.
- [30] Mangueira MCDS, Alves FRV, Catarino PMMC. Hybrid quaternions of Leonardo. Trends in Computational and Applied Mathematics 2022; 23 (1): 51-62. https://doi.org/10.5540/tcam.2022.023.01.00051
- [31] Dumont D. Matrices d'Euler-Siedel. Seminaire Lotharingien de Combinatorie B05c, 1981.
- [32] Dil A, Mezö I. A symmetric algorithm hyperharmonic and Fibonacci numbers. Applied Mathematics and Computation 2008; 206(2): 942-951.
- [33] Graham RL, Knuth DE. Patashnik O.Concrete Mathematics. Addison Wesley 1993.
HYPER-LEONARDO HYBRINOMIALS
Yıl 2023,
Cilt: 11 Sayı: 1, 91 - 103, 28.02.2023
Efruz Özlem Mersin
,
Mustafa Bahşi
Öz
The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.
The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.
The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper-Leonardo hybrid numbers.
Kaynakça
- [1] Falcón S, Plaza Á. On the Fibonacci k-numbers. Chaos, Solitons and Fractals 2007; 32 (5): 1615-1624.
- [2] Yazlik Y, Köme C, Mathusudanan V. A new generalization of Fibonacci and Lucas p-numbers. Journal of Computational Analysis and Applications 2018; 25 (4): 667-669.
- [3] Bernstein M, Sloane NJA. Some canonical sequences of integers. Linear Algebra and its Applications 1995; 226-228: 57-72. https://doi.org/10.1016/0024-3795(94)00245-9
- [4] Betten D. Kalahari and the sequence "Sloane No.377". Annals of Discrete Mathematics 1988; 37: 51-58. https://doi.org/10.1016/S01675060(08)70224-3
- [5] Cameron BJ. Some sequences of integers. Discrete Mathematics 1989; 75 (1-3): 89-102. https://doi.org/10.1016/0012-365X(89)90081-2
- [6] Koshy T. Fibonacci and Lucas numbers with applications. Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs and Tracts, New York: Wiley 2001.
- [7] Catarino PM, Borges A. On Leonardo numbers. Acta Mathematica Universitatis Comenianae 2020; 89 (1): 75-86.
- [8] Alp Y., Koçer GE. Hybrid Leonardo numbers. Chaos, Solitons and Fractals 2021;150: 111128. https://doi.org/10.1016/j.chaos.2021.111128
- [9] Soykan Y. Generalized Leonardo number. Journal of Progressive Research in Mathematics 2021; 18 (4): 58-84.
- [10] Soykan Y. Special cases of generalized Leonardo numbers: modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo numbers. Earthline Journal of Mathematical Sciences 2023; 11(2): 317-342.
- [11] Mersin EÖ, Bahşi M. Hyper-Leonardo numbers. Conference Proceedings of Science and Technology 2022; 5 (1): 14-20.
- [12] Shannon A.G. A note on generalized Leonardo numbers. Notes on Number Theory and Discrete Mathematics 2019; 25 (3): 97-101.
- [13] Kürüz F, Dağdeviren A. Catarino P. On Leonardo Pisano Hybrinomials. Mathematics 2021; 9 (22): 2923. https://doi.org/10.3390/math9222923
- [14] Mersin EÖ. Hyper-Leonardo polynomials. 9th International Congress on Fundamental and Applied Sciences (ICFAS2022) Proceeding book, icfas2022.intsa.org, ISBN 978-605-67052-7-4
- [15] Özdemir M. Introduction to hybrid numbers. Advances in Applied Clifford Algebras 2018; 28 (1): 1-32.
- [16] Szynal-Liana A. Wloch I. The Fibonacci hybrid numbers. Utilitas Mathematica 2019; 110.
- [17] Szynal-Liana A, Wloch I. Introduction to Fibonacci and Lucas hybrinomials. Complex Variables and Elliptic Equations 2020; 65(10): 1736-1747.
- [18] Szynal-Liana A, Wloch I. On Jacopsthal and Jacopsthal-Lucas hybrid numbers. Annales Mathematicae Silesianae 2019; 33: 276-283. https://doi.org/10.2478/amsil-2018-0009
- [19] Szynal-Liana A. The Horadam hybrid numbers. Discussiones Mathematicae General Algebra and Applications 2018; 38(1): 91-98.
- [20] Kızılateş C. A note on Horadam hybrinomials. Fundamental Journal of mathematics and Applications 2022; 5 (1): 1-9. https://doi.org/10.33401/fujma.993546
- [21] Öztürk İ, Özdemir M. Similarity of hybrid numbers. Mathematical Methods in Applied Sciences. 2020; 43(15): 8867-8881. https://doi.org/10.1002/mma.6580
- [22] Yağmur T. A note on generalized hybrid tribonacci numbers. Discussiones Mathematicae General Algebra and Applications 2020; 40:187-199.
[23] Dos Santos Mangueira MC, Vieira RPM, Alves FRV, Catarino PMMC. The hybrid numbers of Padovan and some identities. Annales Mathematicae Silesianae 2020; 34 (2): 256-267. https://doi.org/10.2478/amsil-2020-0019
- [24] Kızılateş C, A new generalization of Fibonacci hybrid and Lucas hybrid numbers. Chaos, Solitons and Fractals 2020; 130: 109449. https://doi.org/10.1016/j.chaos.2019.109449
- [25] Kızılateş C, Kone T. On higher order Fibonacci hyper complex numbers. Chaos, Solitons and Fractals 2021; 148; 111044. https://doi.org/10.1016/j.chaos.2021.111044
[26] Polatlı E. A note on ratios of Fibonacci hybrid and Lucas hybrid numbers. Notes on Number Theory and Discrete Mathematics 2021; 27 (3): 73-78.
- [27] Kızılateş C, Kone T. On special spacelike hybrid numbers with Fibonacci divisor number components. Indian Journal of Pure and Apllied Mathematics 2022;1-9.
- [28] Alp Y, Koçer GE. Hybrid Leonardo numbers. Chaos, Solitons and Fractals 2021; 150: 111128. https://doi.org/10.1016/j.chaos.2021.111128
- [29] Dağdeviren A, Kürüz F. On The Horadam Hybrid Quaternions. arXiv preprint 2020; arXiv:2012.08277.
- [30] Mangueira MCDS, Alves FRV, Catarino PMMC. Hybrid quaternions of Leonardo. Trends in Computational and Applied Mathematics 2022; 23 (1): 51-62. https://doi.org/10.5540/tcam.2022.023.01.00051
- [31] Dumont D. Matrices d'Euler-Siedel. Seminaire Lotharingien de Combinatorie B05c, 1981.
- [32] Dil A, Mezö I. A symmetric algorithm hyperharmonic and Fibonacci numbers. Applied Mathematics and Computation 2008; 206(2): 942-951.
- [33] Graham RL, Knuth DE. Patashnik O.Concrete Mathematics. Addison Wesley 1993.