On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

Authors

Tian-Xiao He, Illinois Wesleyan UniversityFollow
Peter Shiue

Publication Date

September 2009

Comments

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

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