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

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.

References in corpus (2)

• Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series
• q-Lucas polynomials and associated Rogers-Ramanujan type identities