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

Abstract EN

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.