A Q-analog of the BI-periodic lucas sequence | Zendy

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A Q-analog of the BI-periodic lucas sequence

Author(s) -

TAN Elif

Publication year - 2018

Publication title -

communications faculty of science university of ankara series a1mathematics and statistics

Language(s) - English

Resource type - Journals

ISSN - 1303-5991

DOI - 10.1501/commua1_0000000876

Subject(s) - fibonacci number , lucas number , periodic sequence , fibonacci polynomials , sequence (biology) , lucas sequence , mathematics , recurrence relation , representation (politics) , combinatorics , simple (philosophy) , discrete mathematics , pure mathematics , mathematical analysis , orthogonal polynomials , difference polynomials , philosophy , epistemology , biology , politics , political science , law , genetics

In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formulas for the q-bi-periodic Fibonacci and Lucas sequences, we introduce q-analogs of the bi-periodic incomplete Fibonacci and Lucas sequences and give a relation between them.

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