In this paper, firstly, we define the $Q_{q}$ \textit{-generating matrix} for bi-periodic Fibonacci polynomial. And we give $n$th power, determinant and some properties of the bi-periodic Fibonacci polynomial by considering this matrix representation. Also, we introduce the Hadamard products for bi-periodic Fibonacci $Q_{q}^{n}$ generating matrix and bi-periodic Lucas $Q_{l}^{n}$ generating matrix of which entries are bi-periodic Fibonacci and Lucas numbers. Then, we investigate some properties of these products.
bi-periodic Fibonacci numbers bi-periodic Lucas numbers Fibonacci Q matrix matrix method bi-periodic Fibonacci polynomial generating matrix
Primary Language | English |
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Subjects | Engineering |
Journal Section | Articles |
Authors | |
Publication Date | October 15, 2018 |
Submission Date | November 6, 2017 |
Acceptance Date | October 3, 2018 |
Published in Issue | Year 2018 Volume: 6 Issue: 2 |