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A different approach to Gauss Fibonacci polynomials
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In this paper with the help of higher order Fibonacci polynomials, we introduce higher order Gauss Fibonacci polynomials that generalize the Gauss Fibonacci polynomials studied by Özkan and Taştan. We give a recurrence relation, Binet-like formula, generating and exponential generating functions, summation formula for the higher order Gauss Fibonacci polynomials. Moreover, we give two special matrices that we call $Q^{(s)}(x)$ and $P^{(s)}(x),$ respectively. From these matrices, we obtain a matrix representation and derive the Cassini's identity of higher order Gauss Fibonacci polynomials.
Title: A different approach to Gauss Fibonacci polynomials
Description:
In this paper with the help of higher order Fibonacci polynomials, we introduce higher order Gauss Fibonacci polynomials that generalize the Gauss Fibonacci polynomials studied by Özkan and Taştan.
We give a recurrence relation, Binet-like formula, generating and exponential generating functions, summation formula for the higher order Gauss Fibonacci polynomials.
Moreover, we give two special matrices that we call $Q^{(s)}(x)$ and $P^{(s)}(x),$ respectively.
From these matrices, we obtain a matrix representation and derive the Cassini's identity of higher order Gauss Fibonacci polynomials.
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