#### 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

Applied Mathematics | Mathematics

#### Recommended Citation

He, Tian-Xiao and Shiue, Peter, "On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2" (2009). *Scholarship*. 31.

https://digitalcommons.iwu.edu/math_scholarship/31

## Comments

The

International Journal of Mathematics and Mathematical Sciencesis published by Hindawi Publishing Corporation, http://www.hindawi.com/.