On Complex Pulsating Fibonacci Sequence

In this study, we defined complex pulsating Fibonacci sequence of the second kind which is a generalization of first kind. For this newly defined complex sequence we give some summation formulas. In addition, we defined multiplicative version of complex pulsating Fibonacci sequence of second kind.

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  • [1] Ahlfors, L. V. Complex analysis: an introduction to the theory of analyticfunctions of one complex variable. 1953.
  • [2] Alongkot Suvarnamani and Sakunna Koyram. Multiplicative pulsatedfibonacci sequences part 2. Universal Journal of Applied Mathematics 3, 5(2015), 89–93.
  • [3] Fredy D. Neeser and James L. Massey. Proper complex random processeswith applications to information theory. IEEE transactions on informationtheory 39, 4 (1993), 1293–1302.8 Serpil HALICI and Adnan KARATAS ¸
  • [4] Hirose, A. Complex-valued neural networks: theories and applications., vol. 5.2003.
  • [5] Hiroyuki Aoki and Yukio Kosugi. An image storage system using complex-valued associative memories. 15th International Conference on Pattern Recog-nition IEEE 2 (2000), 626–629.
  • [6] Jurgen Haring and AJ Han Vinck. Iterative decoding of codes over com-plex numbers for impulsive noise channels. IEEE Transactions on InformationTheory 49, 5 (2003), 1251–1260.
  • [7] Koshy, T. Fibonacci and Lucas numbers with applications. 2011.
  • [8] Krassimir T. Atanassov. Pulsating fibonacci sequences. Notes on NumberTheory and Discrete Mathematics 19, 3 (2013), 12–14.
  • [9] Margrit Betke and Leonid Gurvits. Mobile robot localization using land-marks. IEEE transactions on robotics and automation 13, 2 (1997), 251–263.
  • [10] Shikha Bhatnagar and Omprakash Sikhwal. Additive pulsating fibonaccisequences and some results. SCIREA Journal of Mathematics 1, 1 (2016), 149–160.