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On Bicomplex Pell and Pell-Lucas Numbers

Yıl 2018, Cilt: 1 Sayı: 2, 142 - 155, 24.12.2018

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.439752
Cited By: 4

Öz

In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected between bicomplex numbers and Pell and Pell-Lucas numbers are investigated. Furthermore, d'Ocagne's identity, Binet's formula, Cassini's identity and Catalan's identity for these numbers are given.

Anahtar Kelimeler

Pell and Pell-Lucas numbers Bicomplex number Quaternion

Kaynakça

  • [1] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), 413–467, doi:10.1007/bf01443559.
  • [2] G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, Inc. New York, 1991.
  • [3] D. Rochon, A Generalized mandelbrot set for bicomplex numbers, Fractals, 8 (2000), 355–368.
  • [4] S. Ö . Karakus, K. F. Aksoyak, Generalized bicomplex numbers and lie groups, Adv. Appl. Clifford Algebr., 25 (2015), 943–963.
  • [5] D. Rochon, M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, Ann. Univ. Oradea Fasc. Mat., 11 (2004), 71–110.
  • [6] M. Bicknell, A primer of the Pell sequence and related sequences, Fibonacci Quart., 13 (1975), 345–349.
  • [7] A. F. Horadam, Pell identities, Fibonacci Quart., 9 (1971), 245–252.
  • [8] R. Melham, Sums Involving Fibonacci and Pell numbers, Port. Math., 56 (1999), 309–317.
  • [9] Z. Şiar, R. Keskin, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat., 42(3) (2013), 211–222.
  • [10] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory, (2018), doi: org/10.1007/s40315-018-0251-5.

Yıl 2018, Cilt: 1 Sayı: 2, 142 - 155, 24.12.2018

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.439752
Cited By: 4

Öz

Kaynakça

  • [1] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), 413–467, doi:10.1007/bf01443559.
  • [2] G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, Inc. New York, 1991.
  • [3] D. Rochon, A Generalized mandelbrot set for bicomplex numbers, Fractals, 8 (2000), 355–368.
  • [4] S. Ö . Karakus, K. F. Aksoyak, Generalized bicomplex numbers and lie groups, Adv. Appl. Clifford Algebr., 25 (2015), 943–963.
  • [5] D. Rochon, M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, Ann. Univ. Oradea Fasc. Mat., 11 (2004), 71–110.
  • [6] M. Bicknell, A primer of the Pell sequence and related sequences, Fibonacci Quart., 13 (1975), 345–349.
  • [7] A. F. Horadam, Pell identities, Fibonacci Quart., 9 (1971), 245–252.
  • [8] R. Melham, Sums Involving Fibonacci and Pell numbers, Port. Math., 56 (1999), 309–317.
  • [9] Z. Şiar, R. Keskin, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat., 42(3) (2013), 211–222.
  • [10] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory, (2018), doi: org/10.1007/s40315-018-0251-5.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Fügen Torunbalcı Aydın

Yayımlanma Tarihi 24 Aralık 2018
Gönderilme Tarihi 2 Temmuz 2018
Kabul Tarihi 2 Ekim 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Torunbalcı Aydın, F. (2018). On Bicomplex Pell and Pell-Lucas Numbers. Communications in Advanced Mathematical Sciences, 1(2), 142-155. https://doi.org/10.33434/cams.439752
AMA Torunbalcı Aydın F. On Bicomplex Pell and Pell-Lucas Numbers. Communications in Advanced Mathematical Sciences. Aralık 2018;1(2):142-155. doi:10.33434/cams.439752
Chicago Torunbalcı Aydın, Fügen. “On Bicomplex Pell and Pell-Lucas Numbers”. Communications in Advanced Mathematical Sciences 1, sy. 2 (Aralık 2018): 142-55. https://doi.org/10.33434/cams.439752.
EndNote Torunbalcı Aydın F (01 Aralık 2018) On Bicomplex Pell and Pell-Lucas Numbers. Communications in Advanced Mathematical Sciences 1 2 142–155.
IEEE F. Torunbalcı Aydın, “On Bicomplex Pell and Pell-Lucas Numbers”, Communications in Advanced Mathematical Sciences, c. 1, sy. 2, ss. 142–155, 2018, doi: 10.33434/cams.439752.
ISNAD Torunbalcı Aydın, Fügen. “On Bicomplex Pell and Pell-Lucas Numbers”. Communications in Advanced Mathematical Sciences 1/2 (Aralık 2018), 142-155. https://doi.org/10.33434/cams.439752.
JAMA Torunbalcı Aydın F. On Bicomplex Pell and Pell-Lucas Numbers. Communications in Advanced Mathematical Sciences. 2018;1:142–155.
MLA Torunbalcı Aydın, Fügen. “On Bicomplex Pell and Pell-Lucas Numbers”. Communications in Advanced Mathematical Sciences, c. 1, sy. 2, 2018, ss. 142-55, doi:10.33434/cams.439752.
Vancouver Torunbalcı Aydın F. On Bicomplex Pell and Pell-Lucas Numbers. Communications in Advanced Mathematical Sciences. 2018;1(2):142-55.

Cited By

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Some properties of bicomplex Pell and Pell-Lucas numbers
Journal of Information and Optimization Sciences
https://doi.org/10.1080/02522667.2020.1814495
A NOTE ON BIGAUSSIAN PELL AND PELL-LUCAS NUMBERS
Journal of Science and Arts
https://doi.org/10.46939/J.Sci.Arts-21.3-a07
Dual-hyperbolic Pell quaternions
Journal of Discrete Mathematical Sciences and Cryptography
https://doi.org/10.1080/09720529.2020.1758367
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