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

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 (U_{n}(a,b;p,q))_{n≥0} or briefly (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.

References

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