3阶广义Fibonacci和Lucas复数  

On the 3-Generalized Fibonacci and Lucas Complex Numbers

作　　者：杨衍婷 赵建堂[1] YANG Yanting;ZHAO Jiantang(School of Mathematics and Statistics,Xianyang Normal University,Xianyang 712000,Shaanxi,China)

机构地区：[1]咸阳师范学院数学与统计学院,陕西咸阳712000

出　　处：《咸阳师范学院学报》2023年第4期11-14,共4页Journal of Xianyang Normal University

基　　金：陕西省自然科学基础研究计划项目(2023JCYB082);陕西省教育科学“十四五”规划课题(SGH22Y1441);咸阳师范学院教改项目(2021Y008)。

摘　　要：将3阶广义Fibonacci和Lucas数的定义推广到3阶广义Fibonacci和Lucas复数,给出了3阶广义Fibonacci和Lucas复数之间的递推关系,研究了3阶广义Fibonacci和Lucas复数的生成函数和Binet型公式,同时,借助Binet型公式得到了Vajda,Catalan,Cassini以及d'Ocagne恒等式,这些恒等式的获得有助于研究广义Fibonacci和Lucas复数。The definition of 3-generalized Fibonacci and Lucas numbers is extended to 3-generalized Fibonacci and Lucas complex numbers.The recurrence relation between 3-generalized Fibonacci and Lucas complex numbers is given.The generating function and the Binet-type formula of 3-generalized Fibonacci and Lucas complex numbers are studied.At the same time,with the help of Binet type formula,some identities such as Vajda’s identity,Catalan’s identity,Cassini’s identity,and d’Ocagne’s identity are derived which can help us to study some properties of these complex numbers.

关 键 词：Fibonacci复数 Lucas复数 Binet型公式 生成函数 

分 类 号：O15[理学—数学]