Construction of generating functions of the products of Vieta polynomials with Gaussian numbers and polynomials

Document Type : Research Paper

Authors

1 LMAM Laboratory and Department of Mathematics‎, ‎Mohamed Seddik Ben Yahia University‎, ‎Jijel‎, ‎Algeria

2 LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria

3 LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria.

10.22075/ijnaa.2021.4868

Abstract

‎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.

Keywords