• ### Generalized Chebyshev Polynomials Via Matrices and Combinatorial Forms of Their Derivatives

Inci GULTEKIN and Betul SAKIROGLU

1. Departmentof Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum, Turkey.

2. Departmentof Mathematics, Science Institute, Atatürk University, 25240 Erzurum, Turkey.

Abstract: In this paper, we obtain the generalized Chebyshev polynomials Vn,m(x) and Ωn,m(x) via matrices and then we define new recurrence relation for the derivative of these polynomials. Also, we give combinatorial forms for the derivatives of these polynomials. Then we create tables for derivative polynomial with the help of combinatorial forms. Finally, we give examples showing how to write derivative polynomials easily.

Keywords: Chebyshev polynomials, Vieta-Fibonacci polynomials, Vieta-Lucas polynomials, determinant, matrix.