论文标题
一些关于斐波那契 - 卢卡斯身份的注释
Some notes on a Fibonacci-Lucas identity
论文作者
论文摘要
在2016年，埃德加（Edgar）和他独立于他，Bhatnagar sta \ tude fibonacci和Lucas数字是一个不错的多项式身份。出版物后不久，这种身份已通过两种不同的方式进行了推广：Dafnis，Phillipou和Livieris对fibonacci序列$ k $和ABD-ELHAMEED和ZEYADA EDGAREDED EDGAR-BHATNAGAR的序列提供了概括，以向普通的菲菲比诺卡奇和Lucas序列。在本文中，我们为广义卢卡斯序列提供了更多的多项式身份。我们讨论有趣的方面和特殊案例，这些方面尚未说明，但值得认可。最后，我们证明了Chebyshev多项式的这些身份的多项式类似物。
In 2016, Edgar and, independently of him, Bhatnagar sta\-ted a nice polynomial identity that connects Fibonacci and Lucas numbers. Shortly after their publications, this identity has been generalized in two different ways: Dafnis, Phillipou and Livieris provided a generalization to Fibonacci sequences of order $k$ and Abd-Elhameed and Zeyada extended Edgar--Bhatnagar identity to generalized Fibonacci and Lucas sequences. In this paper, we present more polynomial identities for generalized Lucas sequences. We discuss interesting aspects and special cases which have not been stated before but deserve recognition. Finally, we prove the polynomial analogues of these identities for Chebyshev polynomials.
