论文标题
动态卢卡斯序列的椭圆溶液
Elliptic solutions of dynamical Lucas sequences
论文作者
论文摘要
我们研究了Lucas序列的两种类型的动力扩展，并为它们提供了椭圆溶液。第一种类型涉及涉及通勤变量的级别依赖性（或离散的时间依赖性）版本。我们表明，该系统的一个不错的解决方案由椭圆数给出。第二种类型涉及卢卡斯序列的非交通性版本，该版本定义了约翰·雪茄（Johann Cigler）引入的非交换性（或抽象）斐波那契多项式。如果非交易变量专门为椭圆形变量，则抽象的fibonacci多项式将成为非交换性椭圆纤维纤维多项式。我们得出的某些特性包括它们在归一化的单元和非共同椭圆形的Euler--Cassini身份方面的显式扩展。
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler--Cassini identity.
