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.