SOME NOTES ON A FIBONACCI-LUCAS IDENTITY
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In 2016, Edgar and, independently of him, Bhatnagar stated a nice polynomial identity that connects Fibonacci and Lucas numbers. Shortly after their publications, this identity was generalized in two different ways: Dafnis, Phillipou and Livieris provided a generalization to Fibonacci sequences of order k, while Abd-Elhameed and Zeyada extended the 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.
Abstract
In 2016, Edgar and, independently of him, Bhatnagar stated a nice polynomial identity that connects Fibonacci and Lucas numbers. Shortly after their publications, this identity was generalized in two different ways: Dafnis, Phillipou and Livieris provided a generalization to Fibonacci sequences of order k, while Abd-Elhameed and Zeyada extended the 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.
참고문헌 (20)
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