Geodesic
On the expansion of Fibonacci and Lucas polynomials
Journal of integer sequences, Tome 12 (2009) no. 1
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 
@article{JIS_2009__12_1_a5,
     author = {Prodinger,  Helmut},
     title = {On the expansion of {Fibonacci} and {Lucas} polynomials},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {1},
     zbl = {1228.11022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_1_a5/}
}
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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/