广义高斯Fibonacci和Lucas多项式及其恒等式

Generalized Gaussian Fibonacci and Lucas Polynomials and Their Identities

本文给出了广义高斯斐波那契多项式和广义高斯卢卡斯多项式的定义。我们研究了它们的一些的性质,通过它们的递推关系和性质及矩阵表示,我们也得到了它们之间的一些恒等式。此外,我们还证明了相应的卡西尼恒等式。

In this paper, we give the definition of Generalized Gaussian Fibonacci polynomials and Generalized Gaussian Lucas polynomials. We obtain some exciting properties of them, by their recurrence relation and properties and matrix representations, we also obtain some identities of them. Fur-thermore, we prove Cassini’s Identities for them and their polynomials.