On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers

  • Engin Özkan Erzincan Binali Yıldırım University
  • Bahar Kuloğlu Erzincan Binali Yıldırım University
Keywords: Bicomplex numbers, Gaussian Fibonacci numbers, bicomplex Gaussian Fibonacci numbers, Binet’s formula.

Abstract

We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers.

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Author Biography

Bahar Kuloğlu, Erzincan Binali Yıldırım University

Graduate School of Natural and Applied Sciences

Published
2022-05-28
Section
Articles