A new class of generating functions of binary products of Gaussian numbers and polynomials

Authors : Souhila BOUGHABA, Ali BOUSSAYOUD, Mohamed KERADA

Pages : 1240-1255

Doi:10.31801/cfsuasmas.597653

View : 11 | Download : 5

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :In this paper, we introduce a operator in order to derive some new symmetric properties of Gaussian Fibonacci numbers and Gaussian Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions for Gaussian Fibonacci numbers and Gaussian Jacobsthal polynomials. In the paper Al4, Al5, a second-order linear recurrence sequence insert ignore into journalissuearticles values(U_{n}insert ignore into journalissuearticles values(a,b;p,q););_{n≥0} or briefly insert ignore into journalissuearticles values(U_{n});_{n≥0} is considered by the recurrence relation: U_{n+2}=pU_{n+1}+qU_{n}, with the initial conditions U₀=a and U₁=b, where a,b∈ℂ and p,q∈ℤ₊ for n≥0.
Keywords : Symmetric functions, generating functions, Gaussian Fibonacci numbers, Gaussian Lucas numbers