$(p,q)-$deformed Fibonacci and Lucas polynomials: characterization and Fourier integral transforms (1307.2623v1)

Abstract: A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed and discussed. Relevant results known in the literature are examined as particular cases.