On Bicomplex Pell and Pell-Lucas Numbers
Abstract
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.
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References
- [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.
