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arXiv · 1207.5891

Derivations and identities for Fibonacci and Lucas polynomials

Leonid Bedratyuk
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Abstract

We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any polynomial identity for Appel polynomial yields a polynomial identity for the Fibonacci and Lucas polynomials and describe the corresponding intertwining maps.

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Leonid Bedratyuk. 2012-07-25. Derivations and identities for Fibonacci and Lucas polynomials. https://arxiv.org/abs/1207.5891

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