Geodesic
On the expansion of Fibonacci and Lucas polynomials
Journal of integer sequences, Tome 12 (2009) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Recently, Belbachir and Bencherif have expanded Fibonacci and Lucas polynomials using bases of Fibonacci- and Lucas-like polynomials. Here, we provide simplified proofs for the expansion formulae that in essence a computer can do. Furthermore, for 2 of the 5 instances, we find $q$-analogues.
Classification : 11B39, 11B37
Keywords: Fibonacci polynomials, Lucas polynomials, generating functions, q-analogues 
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     author = {Prodinger, Helmut},
     title = {On the expansion of {Fibonacci} and {Lucas} polynomials},
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Prodinger, Helmut. On the expansion of Fibonacci and Lucas polynomials. Journal of integer sequences, Tome 12 (2009) no. 1. http://geodesic.mathdoc.fr/item/JIS_2009__12_1_a5/