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Dual-complex generalized k-Horadam numbers

Yıl 2021, Cilt: 70 Sayı: 1, 117 - 129, 30.06.2021
https://doi.org/10.31801/cfsuasmas.780861

Öz

The purpose of this paper is to provide a broad overview of the generalization of the various dual-complex number sequences, especially in the disciplines of mathematics and physics. By the help of dual numbers and dual-complex numbers, in this paper, we define the dual-complex generalized k-Horadam numbers. Furthermore, we investigate the Binet formula, generating function, some conjugation identities, summation formula and a theorem which is generalization of the Catalan's identity, Cassini's identity and d'Ocagne's identity.

Kaynakça

  • Aydın, F. T., Dual−complex k−Fibonacci numbers, Chaos, Solitons & Fractals, 115 (2018), 1–6.
  • Aydın, F. T., Dual−complex k−Pell quaternions, arXiv preprint arXiv:1810.05002 (2018).
  • Brodsky, V., Shoham, M., Dual numbers representation of rigid body dynamics, Mechanism and machine theory, 34 (5) (1999), 693–718.
  • Clifford, W. K., A preliminary sketch of biquaternions, 1873.
  • Dimentberg, F. M., The screw calculus and its applications in mechanics, Foreign Technology Division, 1969.
  • Falcon, S., On the k−Lucas numbers, International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039–1050.
  • Falcón, S., Plaza, Á., The k−Fibonacci sequence and the pascal 2-triangle, Chaos, Solitons & Fractals, 33 (1) (2007), 38-49.
  • Fischer, I., Dual−number methods in kinematics, statics and dynamics, Routledge, 2017.
  • Fjelstad, P., Gal, S. G., n−dimensional dual complex numbers, Advances in Applied Clifford Algebras, 8 (2) (1998), 309–322.
  • Güngör, M. A., Azak, A. Z., Investigation of dual-complex fibonacci, dual-complex lucas numbers and their properties, Advances in Applied Clifford Algebras, 27 (4) (2017), 3083– 3096.
  • Horadam, A., A generalized Fibonacci sequence, The American Mathematical Monthly, 68 (5) (1961), 455–459.
  • Horadam, A., Special properties of the sequence w n (a, b; p, q), The Fibonacci Quarterly, 5 (5) (1967), 424–434.
  • Horadam, A., et al., Generating functions for powers of a certain generalised sequence of numbers, Duke Mathematical Journal, 32 (3) (1965), 437–446.
  • Irmak, N., More identities for Fibonacci and Lucas quaternions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69 (1) (2020), 369–375.
  • Koshy, T., Fibonacci and Lucas numbers with applications. 2001, A Wiley-Interscience Publication.
  • Liu, L., On the spectrum and spectral norms of r−circulant matrices with generalized k−Horadam numbers entries, International Journal of Computational Mathematics, 2014 (2014).
  • Majernik, V., Multicomponent number systems, Acta Physica. Polonica A., 90 (3) (1996), 491–498.
  • Matsuda, G., Kaji, S., Ochiai, H., Anti-commutative dual complex numbers and 2d rigid transformation, In Mathematical Progress in Expressive Image Synthesis I, Springer, 2014, pp. 131–138.
  • Messelmi, F., Dual-complex numbers and their holomorphic functions.
  • Study, E., Geometrie der dynamen, 1903, Study, E., Geometrie der dynamen, 1903.
  • Tan, E., Leung, H.-H., Some results on Horadam quaternions, Chaos, Solitons & Fractals, 138 (2020), 109961.
  • Yazlik, Y., Köme, C., Madhusudanan, V., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25 (4) (2018), 657–669.
  • Yazlik, Y., Köme, S., Köme, C., Bicomplex generalized k−Horadam quaternions, Miskolc Mathematical Notes, 20 (2) (2019), 1315–1330.
  • Yazlik, Y., Taskara, N., A note on generalized k−Horadam sequence, Computers & Mathematics with Applications, 63 (1) (2012), 36–41.
Yıl 2021, Cilt: 70 Sayı: 1, 117 - 129, 30.06.2021
https://doi.org/10.31801/cfsuasmas.780861

Öz

Kaynakça

  • Aydın, F. T., Dual−complex k−Fibonacci numbers, Chaos, Solitons & Fractals, 115 (2018), 1–6.
  • Aydın, F. T., Dual−complex k−Pell quaternions, arXiv preprint arXiv:1810.05002 (2018).
  • Brodsky, V., Shoham, M., Dual numbers representation of rigid body dynamics, Mechanism and machine theory, 34 (5) (1999), 693–718.
  • Clifford, W. K., A preliminary sketch of biquaternions, 1873.
  • Dimentberg, F. M., The screw calculus and its applications in mechanics, Foreign Technology Division, 1969.
  • Falcon, S., On the k−Lucas numbers, International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039–1050.
  • Falcón, S., Plaza, Á., The k−Fibonacci sequence and the pascal 2-triangle, Chaos, Solitons & Fractals, 33 (1) (2007), 38-49.
  • Fischer, I., Dual−number methods in kinematics, statics and dynamics, Routledge, 2017.
  • Fjelstad, P., Gal, S. G., n−dimensional dual complex numbers, Advances in Applied Clifford Algebras, 8 (2) (1998), 309–322.
  • Güngör, M. A., Azak, A. Z., Investigation of dual-complex fibonacci, dual-complex lucas numbers and their properties, Advances in Applied Clifford Algebras, 27 (4) (2017), 3083– 3096.
  • Horadam, A., A generalized Fibonacci sequence, The American Mathematical Monthly, 68 (5) (1961), 455–459.
  • Horadam, A., Special properties of the sequence w n (a, b; p, q), The Fibonacci Quarterly, 5 (5) (1967), 424–434.
  • Horadam, A., et al., Generating functions for powers of a certain generalised sequence of numbers, Duke Mathematical Journal, 32 (3) (1965), 437–446.
  • Irmak, N., More identities for Fibonacci and Lucas quaternions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69 (1) (2020), 369–375.
  • Koshy, T., Fibonacci and Lucas numbers with applications. 2001, A Wiley-Interscience Publication.
  • Liu, L., On the spectrum and spectral norms of r−circulant matrices with generalized k−Horadam numbers entries, International Journal of Computational Mathematics, 2014 (2014).
  • Majernik, V., Multicomponent number systems, Acta Physica. Polonica A., 90 (3) (1996), 491–498.
  • Matsuda, G., Kaji, S., Ochiai, H., Anti-commutative dual complex numbers and 2d rigid transformation, In Mathematical Progress in Expressive Image Synthesis I, Springer, 2014, pp. 131–138.
  • Messelmi, F., Dual-complex numbers and their holomorphic functions.
  • Study, E., Geometrie der dynamen, 1903, Study, E., Geometrie der dynamen, 1903.
  • Tan, E., Leung, H.-H., Some results on Horadam quaternions, Chaos, Solitons & Fractals, 138 (2020), 109961.
  • Yazlik, Y., Köme, C., Madhusudanan, V., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25 (4) (2018), 657–669.
  • Yazlik, Y., Köme, S., Köme, C., Bicomplex generalized k−Horadam quaternions, Miskolc Mathematical Notes, 20 (2) (2019), 1315–1330.
  • Yazlik, Y., Taskara, N., A note on generalized k−Horadam sequence, Computers & Mathematics with Applications, 63 (1) (2012), 36–41.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Sure Köme 0000-0002-3558-0557

Cahit Köme 0000-0002-6488-9035

Yasin Yazlik 0000-0001-6369-540X

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 14 Ağustos 2020
Kabul Tarihi 2 Kasım 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

APA Köme, S., Köme, C., & Yazlik, Y. (2021). Dual-complex generalized k-Horadam numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 117-129. https://doi.org/10.31801/cfsuasmas.780861
AMA Köme S, Köme C, Yazlik Y. Dual-complex generalized k-Horadam numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2021;70(1):117-129. doi:10.31801/cfsuasmas.780861
Chicago Köme, Sure, Cahit Köme, ve Yasin Yazlik. “Dual-Complex Generalized K-Horadam Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 117-29. https://doi.org/10.31801/cfsuasmas.780861.
EndNote Köme S, Köme C, Yazlik Y (01 Haziran 2021) Dual-complex generalized k-Horadam numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 117–129.
IEEE S. Köme, C. Köme, ve Y. Yazlik, “Dual-complex generalized k-Horadam numbers”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 117–129, 2021, doi: 10.31801/cfsuasmas.780861.
ISNAD Köme, Sure vd. “Dual-Complex Generalized K-Horadam Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 2021), 117-129. https://doi.org/10.31801/cfsuasmas.780861.
JAMA Köme S, Köme C, Yazlik Y. Dual-complex generalized k-Horadam numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:117–129.
MLA Köme, Sure vd. “Dual-Complex Generalized K-Horadam Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 117-29, doi:10.31801/cfsuasmas.780861.
Vancouver Köme S, Köme C, Yazlik Y. Dual-complex generalized k-Horadam numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):117-29.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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