Incomplete q-Chebyshev Polynomials

TL;DR

This paper introduces incomplete q-Chebyshev polynomials, deriving their generating functions, explicit formulas, recurrence relations, and exploring their connections to other well-known polynomials.

Contribution

It presents new generalizations called incomplete q-Chebyshev polynomials, along with their properties and relations to existing polynomial families.

Findings

Derived generating functions for q-Chebyshev polynomials

Established recurrence relations and properties

Connected incomplete q-Chebyshev polynomials to known polynomial families

Abstract

In this paper, we get the generating functions of q-Chebyshev polynomials using operator. Also considering explicit formulas of q-Chebyshev polynomials, we give new generalizations of q-Chebyshev polynomials called incomplete q-Chebyshev polynomials of the first and second kind. We obtain recurrence relations and several properties of these polynomials. We show that there are connections between incomplete q-Chebyshev polynomials and the some well-known polynomials. Keywords: q-Chebyshev polynomials, q-Fibonacci polynomials, Incomplete polynomials, Fibonacci number