Araştırma Makalesi
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Yıl 2022, Cilt: 5 Sayı: 1, 1 - 9, 01.03.2022

Can Kızılateş

https://doi.org/10.33401/fujma.993546
Cited By: 8

Öz

Kaynakça

  • [1] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Q., 3 (1965), 161-176.
  • [2] A. F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke Math. J., 32 (1965), 437-446, .
  • [3] T. Koshy, Fibonacci and Lucas Numbers with Applications, Vol. 1, Second edition, Pure and Applied Mathematics (Hoboken), John Wiley & Sons, Inc., Hoboken, NJ, 2018.
  • [4] S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32 (5) (2007), 1615-1624.
  • [5] E. G. Kocer, N. Tuglu, A. Stakhov, On the m-extension of the Fibonacci and Lucas p􀀀numbers, Chaos Solitons Fractals, 40 (4) (2009), 1890-1906.
  • [6] C. Kızılateş, New families of Horadam numbers associated with finite operators and their applications, Math. Meth. Appl. Sci., 44 (2021), 14371-14381.
  • [7] T. Horzum, E. G. Kocer, On some properties of Horadam polynomials, Int. Math. Forum., 25 (4) (2009), 1243-1252.
  • [8] M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebras, 28 (1) (2018).
  • [9] A. Szynal-Liana, I. Wloch, The Fibonacci hybrid numbers, Utilitas Math., 110 (2019), 3-10.
  • [10] A. Szynal-Liana, I. Wloch, On Jacosthal and Jacosthal-Lucas hybrid numbers, Ann. Math. Sil., 33 (1) (2019), 276-283.
  • [11] A. Szynal-Liana, I. Wloch, On Pell and Pell–Lucas Hybrid Numbers, Commentat. Math., 58 (2018), 11-17.
  • [12] A. Szynal-Liana, The Horadam hybrid numbers, Discuss. Math. Gen. Algebra Appl., 38 (1) (2018), 91-98.
  • [13] C. Kızılateş, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos Solitons Fractals, 130 (2020), 1-5.
  • [14] P. Catarino, On k-Pell hybrid numbers, J. Discrete Math. Sci. Cryptography, 22 (1) (2019), 83-89.
  • [15] G. Cerda Moreles, Investigation of generalized hybrid Fibonacci numbers and their properties, Appl. Math. E-Notes, 21 (2021), 110-118.
  • [16] G. Cerda Moreles, Introduction to third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, Discuss. Math. Gen. Algebra Appl., 41 (1) (2021), 139-152.
  • [17] Y. Alp, E. G. Kocer, Hybrid Leonardo numbers, Chaos Solitons Fractals, 150 (2021), 1-5.
  • [18] D. Tasci, E. Sevgi, Some properties between Mersenne, Jacobsthal and Jacobsthal-Lucas hybrid numbers, Chaos Solitons Fractals, 146 (2021), 1-4.
  • [19] E. Tan, NR. Ait-Amrane, On a new generalization of Fibonacci hybrid numbers, (2020), arXiv:2006.09727.
  • [20] S. Petroudi, M. Pirouz, A. Özkoç, The Narayana polynomial and Narayana hybrinomial sequences, Konuralp J. Math., 9 (1) (2021), 90-99.
  • [21] A. Özkoç, A new generalization of Tribonacci hybrinomial, Bull. Int. Math. Virtual Inst., 11 (3) (2021), 555-568.
  • [22] R. Vieira, M. Mangueira, F. R. Alves, P. M. M. Cruz Catarino, Padovan and Perrin Hybrid Number Identities, Commun. Adv. Math. Sci., 4 (4) (2021), 190-197.
  • [23] E. Polatlı, A note on ratios of Fibonacci hybrid and Lucas hybrid numbers, Notes Number Theory Discrete Math., 27 (3) (2021), 73-78.
  • [24] A. Szynal-Liana, I. Wloch, Introduction to Fibonacci and Lucas hybrinomials, Complex Var. Elliptic Eq., 65 (10) (2020), 1736-1747.
  • [25] M. Liana, A. Szynal-Liana, I. Wloch, On Pell hyrinomials, Miskolc Math. Notes, 20 (2019), 1051-1062.
  • [26] S. Falcon, On the generating matrices of the k-Fibonacci numbers, Proyecciones J. Math., 32 (4) (2013), 347-357.
  • [27] P. Catarino, A note on certain matrices with h(x)-Fibonacci quaternion polynomials, J. Differ. Eq. Appl., 22 (2016), 343-351.
  • [28] C. Kızılateş, P. Catarino, N. Tuglu, On the bicomplex generalized Tribonacci quaternions, Mathematics, 7 (1) (2019), 80.
  • [29] C. Kızılateş, A Note on Horadam hybrinomials, (2020), Preprints:2020010116.

A Note on Horadam Hybrinomials

Yıl 2022, Cilt: 5 Sayı: 1, 1 - 9, 01.03.2022

Can Kızılateş

https://doi.org/10.33401/fujma.993546
Cited By: 8

Öz

This paper ensures an extensive survey of the generalization of the various hybrid numbers and hybrid polynomials especially as part of its enhancing importance in the disciplines of mathematics and physics. In this paper, by using the Horadam polynomials, we define the Horadam hybrid polynomials called Horadam hybrinomials. We obtain some special cases and algebraic properties of the Horadam hybrinomials such as recurrence relation, generating function, exponential generating function, Binet formula, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity, respectively. Moreover, we give some applications related to the Horadam hybrinomials in matrices.

Anahtar Kelimeler

Horadam number Horadam polynomial Hybrid number

Kaynakça

  • [1] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Q., 3 (1965), 161-176.
  • [2] A. F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke Math. J., 32 (1965), 437-446, .
  • [3] T. Koshy, Fibonacci and Lucas Numbers with Applications, Vol. 1, Second edition, Pure and Applied Mathematics (Hoboken), John Wiley & Sons, Inc., Hoboken, NJ, 2018.
  • [4] S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32 (5) (2007), 1615-1624.
  • [5] E. G. Kocer, N. Tuglu, A. Stakhov, On the m-extension of the Fibonacci and Lucas p􀀀numbers, Chaos Solitons Fractals, 40 (4) (2009), 1890-1906.
  • [6] C. Kızılateş, New families of Horadam numbers associated with finite operators and their applications, Math. Meth. Appl. Sci., 44 (2021), 14371-14381.
  • [7] T. Horzum, E. G. Kocer, On some properties of Horadam polynomials, Int. Math. Forum., 25 (4) (2009), 1243-1252.
  • [8] M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebras, 28 (1) (2018).
  • [9] A. Szynal-Liana, I. Wloch, The Fibonacci hybrid numbers, Utilitas Math., 110 (2019), 3-10.
  • [10] A. Szynal-Liana, I. Wloch, On Jacosthal and Jacosthal-Lucas hybrid numbers, Ann. Math. Sil., 33 (1) (2019), 276-283.
  • [11] A. Szynal-Liana, I. Wloch, On Pell and Pell–Lucas Hybrid Numbers, Commentat. Math., 58 (2018), 11-17.
  • [12] A. Szynal-Liana, The Horadam hybrid numbers, Discuss. Math. Gen. Algebra Appl., 38 (1) (2018), 91-98.
  • [13] C. Kızılateş, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos Solitons Fractals, 130 (2020), 1-5.
  • [14] P. Catarino, On k-Pell hybrid numbers, J. Discrete Math. Sci. Cryptography, 22 (1) (2019), 83-89.
  • [15] G. Cerda Moreles, Investigation of generalized hybrid Fibonacci numbers and their properties, Appl. Math. E-Notes, 21 (2021), 110-118.
  • [16] G. Cerda Moreles, Introduction to third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, Discuss. Math. Gen. Algebra Appl., 41 (1) (2021), 139-152.
  • [17] Y. Alp, E. G. Kocer, Hybrid Leonardo numbers, Chaos Solitons Fractals, 150 (2021), 1-5.
  • [18] D. Tasci, E. Sevgi, Some properties between Mersenne, Jacobsthal and Jacobsthal-Lucas hybrid numbers, Chaos Solitons Fractals, 146 (2021), 1-4.
  • [19] E. Tan, NR. Ait-Amrane, On a new generalization of Fibonacci hybrid numbers, (2020), arXiv:2006.09727.
  • [20] S. Petroudi, M. Pirouz, A. Özkoç, The Narayana polynomial and Narayana hybrinomial sequences, Konuralp J. Math., 9 (1) (2021), 90-99.
  • [21] A. Özkoç, A new generalization of Tribonacci hybrinomial, Bull. Int. Math. Virtual Inst., 11 (3) (2021), 555-568.
  • [22] R. Vieira, M. Mangueira, F. R. Alves, P. M. M. Cruz Catarino, Padovan and Perrin Hybrid Number Identities, Commun. Adv. Math. Sci., 4 (4) (2021), 190-197.
  • [23] E. Polatlı, A note on ratios of Fibonacci hybrid and Lucas hybrid numbers, Notes Number Theory Discrete Math., 27 (3) (2021), 73-78.
  • [24] A. Szynal-Liana, I. Wloch, Introduction to Fibonacci and Lucas hybrinomials, Complex Var. Elliptic Eq., 65 (10) (2020), 1736-1747.
  • [25] M. Liana, A. Szynal-Liana, I. Wloch, On Pell hyrinomials, Miskolc Math. Notes, 20 (2019), 1051-1062.
  • [26] S. Falcon, On the generating matrices of the k-Fibonacci numbers, Proyecciones J. Math., 32 (4) (2013), 347-357.
  • [27] P. Catarino, A note on certain matrices with h(x)-Fibonacci quaternion polynomials, J. Differ. Eq. Appl., 22 (2016), 343-351.
  • [28] C. Kızılateş, P. Catarino, N. Tuglu, On the bicomplex generalized Tribonacci quaternions, Mathematics, 7 (1) (2019), 80.
  • [29] C. Kızılateş, A Note on Horadam hybrinomials, (2020), Preprints:2020010116.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Can Kızılateş 0000-0002-7958-4226

Erken Görünüm Tarihi 13 Şubat 2022
Yayımlanma Tarihi 1 Mart 2022
Gönderilme Tarihi 9 Eylül 2021
Kabul Tarihi 4 Aralık 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 1

Kaynak Göster

APA Kızılateş, C. (2022). A Note on Horadam Hybrinomials. Fundamental Journal of Mathematics and Applications, 5(1), 1-9. https://doi.org/10.33401/fujma.993546
AMA Kızılateş C. A Note on Horadam Hybrinomials. FUJMA. Mart 2022;5(1):1-9. doi:10.33401/fujma.993546
Chicago Kızılateş, Can. “A Note on Horadam Hybrinomials”. Fundamental Journal of Mathematics and Applications 5, sy. 1 (Mart 2022): 1-9. https://doi.org/10.33401/fujma.993546.
EndNote Kızılateş C (01 Mart 2022) A Note on Horadam Hybrinomials. Fundamental Journal of Mathematics and Applications 5 1 1–9.
IEEE C. Kızılateş, “A Note on Horadam Hybrinomials”, FUJMA, c. 5, sy. 1, ss. 1–9, 2022, doi: 10.33401/fujma.993546.
ISNAD Kızılateş, Can. “A Note on Horadam Hybrinomials”. Fundamental Journal of Mathematics and Applications 5/1 (Mart 2022), 1-9. https://doi.org/10.33401/fujma.993546.
JAMA Kızılateş C. A Note on Horadam Hybrinomials. FUJMA. 2022;5:1–9.
MLA Kızılateş, Can. “A Note on Horadam Hybrinomials”. Fundamental Journal of Mathematics and Applications, c. 5, sy. 1, 2022, ss. 1-9, doi:10.33401/fujma.993546.
Vancouver Kızılateş C. A Note on Horadam Hybrinomials. FUJMA. 2022;5(1):1-9.

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 Kapak Resmi İndir

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