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

TL;DR

This paper fully characterizes $(p,q)$-deformed Fibonacci and Lucas polynomials, exploring their recursion relations, generating functions, and Fourier transforms, and relates these findings to existing literature.

Contribution

It provides a comprehensive characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials, including explicit formulas for their generating functions and Fourier transforms.

Findings

Explicit generating functions derived

Fourier integral transforms computed and discussed

Connections to known results examined

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.