k. -佩尔-卢卡斯混合数与 k. -佩尔-卢卡斯混合多项式的代数性质

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中图分类号：0015 文献标志码：A

Algebraic Properties of k -Pell-Lucas Hybrid Numbers and （2号 -Pell-Lucas Hybrid Polynomials

DENG Yong， CHEN Quanguo

（College of Mathematics and Statistics，Kashi University，Kashi 844OOO，Xinjiang，China）

Abstract： To extend concepts of k -Pell-Lucas progressions and k -Pell-Lucas polynomial sequences，notions of k -PellLucas hybrid numbers and k -Pell-Lucas hybrid polynomials were introduced by considering k -Pell-Lucas progressions and k -Pell-Lucas polynomial sequences as components of hybrid numbers. Concepts of k -Pell-Lucas hybrid progressions and k -Pell-Lucas hybrid polynomial sequences were further derived. Binet formula for k -Pell-Lucas hybrid numbers and k -Pell-Lucas hybridpolynomials，aswellasgenerating functions，exponential generatingfunctions，andVajdaidentities for k -Pell-Lucas hybrid progressions and k -Pell-Lucas hybrid polynomial sequences were discussed. The results show that Binet formula for k -Pell-Lucas hybrid numbers and exponential generating functions for k -Pell-Lucas hybrid progressions are determined by roots of characteristic equations for k -Pell-Lucas progressions and hybrid numbers. Generating functions for k -Pell-Lucas hybrid progressions can be expressed as functions related to initial conditions for k -Pell-Lucas hybrid progressions， and k -Pell-Lucas hybrid polynomial sequences exhibit algebraic properties similar to those of k -Pell-Lucas hybrid progressions.

Keywords： hybrid number； algebraic property； k -Pell -Lucas hybrid number； k -Pell -Lucashybrid polynomial; recurrence relation

斐波那契（Fibonacci）数列与卢卡斯（Lucas）数列近年来广泛应用于线性代数、应用数学、微积分等数学分支。（剩余5593字）