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A Note on Fibonacci & Lucas and
Bernoulli & Euler Polynomials Claudio de Jesús Pita Ruiz Velasco
Universidad Panamericana
Mexico City, Mexico
mailto:cpita@up.edu.mxcpita@up.edu.mx

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Abstract:

We study certain polynomials $P_{m}\left( x,y;t\right)$ and $Q_{m}\left( x,y;t\right)$ of the variable $t$ whose coefficients involve bivariate Fibonacci polynomials $F_{j}\left( x,y\right)$ or bivariate Lucas polynomials $L_{j}\left( x,y\right)$. By working with $P_{m}\left( x,y;tx\right)$ and $Q_{m}\left( x,y;tx\right)$, together with the generating functions for Bernoulli polynomials $B_{i}\left( t\right)$ and Euler polynomials $E_{i}\left( t\right)$, we obtain a list of eight identities connecting $F_{j}\left( x,y\right)$ or $L_{j}\left( x,y\right)$ with $B_{i}\left( t\right)$ or $E_{i}\left( t\right)$. We present also some consequences of these results.