Article
On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
International Journal of Mathematics and Mathematical Sciences
(2009)
Abstract
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a generalmethod to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.
Disciplines
Publication Date
Fall September, 2009
Publisher Statement
The International Journal of Mathematics and Mathematical Sciences is published by Hindawi Publishing Corporation, http://www.hindawi.com/.
Citation Information
Tian-Xiao He and Peter J.-S. Shiue. "On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2" International Journal of Mathematics and Mathematical Sciences Vol. 2009 (2009) Available at: http://works.bepress.com/tian_xiao_he/21/