New families of generating functions for Q-fibonacci and the related polynomials

In this paper, several families of multilinear and multilateral generating functions for Fibonacci and Lucas polynomials based on g-integers are derived. Then some special cases are given. © 2018 Charles Babbage Research Centre. All rights reserved

On the (p, q)-Chebyshev polynomials and related polynomials

In this paper, we introduce ( p , q ) ⁻Chebyshev polynomials of the first and second kind that reduces the ( p , q ) ⁻Fibonacci and the ( p , q ) ⁻Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived

On the (p, q)-Chebyshev polynomials and related polynomials

In this paper, we introduce (p, q)-Chebyshev polynomials of the first and second kind that reduces the (p, q)-Fibonacci and the (p, q)-Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived. © 2019 by the authors

New families of three-variable polynomials coupled with well-known polynomials and numbers

In this paper, firstly the definitions of the families of three-variable polynomials with the new generalized polynomials related to the generating functions of the famous polynomials and numbers in literature are given. Then, the explicit representation and partial differential equations for new polynomials are derived. The special cases of our polynomials are given in tables. In the last section, the interesting applications of these polynomials are found. © 2019 by the authors