Some Relationships among Vieta, Morgan-Voyce and Jacobsthal Polynomials

@inproceedings{Shannon1999SomeRA,
title={Some Relationships among Vieta, Morgan-Voyce and Jacobsthal Polynomials},
author={A. Shannon and A. F. Horadam},
year={1999}
}

We define below the Morgan-Voyce polynomials B n(x) and b n(x) [21], and the ‘companion’ Morgan-Voyce polynomials C n(x) and c n(x) which were found in embryonic form in [26] and formalized, particularly in terms of notation, by Horadam [12, 16]. Horadam [11, 13] has also developed properties for the Jacobsthal polynomials, J n(x). It is the purpose of this paper to reveal some new inter-relationships among these polynomials and between them and the Fibonacci and Lucas numbers.