Construction of Generating Functions of the Products of Vieta Polynomials with Gaussian Numbers and Polynomials

‎In the present paper‎, ‎we introduce the recurrence relations of Vieta‎ ‎Fibonacci‎, ‎Vieta Lucas‎, ‎Vieta Pell and Vieta Pell Lucas polynomials‎. ‎We‎ obtain the generating functions of these polynomials‎, ‎then we give the new‎ ‎generating functions of the products of these polynomials and the products‎ ‎of these polynomials with Gaussian numbers and polynomials‎. ‎These results‎ ‎are based on the relation between Vieta polynomials and Chebyshev‎ ‎polynomials of first and second kinds‎.