Journal of Integer Sequences, Vol. 15 (2012), Article 12.2.7

A Note on Fibonacci & Lucas and Bernoulli & Euler Polynomials


Claudio de Jesús Pita Ruiz Velasco
Universidad Panamericana
Mexico City, Mexico

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.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000032 A000045)

Received September 9 2011; revised versions received December 8 2011; January 13 2012. Published in Journal of Integer Sequences, January 14 2012.

Return to Journal of Integer Sequences home page