On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
Open Access
- 25 October 2009
- journal article
- research article
- Published by Hindawi Limited in International Journal of Mathematics and Mathematical Sciences
- Vol. 2009, 1-21
- https://doi.org/10.1155/2009/709386
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 general method 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.Keywords
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