Abstract
The three — term recurrence xn + yn = (x + y) · (xn−1 + yn−1) − xy · (xn−2 + yn−2) allows to express xn + yn as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebraically via the Girard — Waring formula, combinatorially via Lucas numbers and polynomials, and analytically as a special orthogonal polynomial. We shall briefly describe all these aspects and present an application from number theory.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
