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**On sequences of numbers and polynomials defined by linear recurrence relations of order 2.**
*(English)*
Zbl 1193.11014

Summary: 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.

### MSC:

11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |

11C08 | Polynomials in number theory |

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\textit{T.-X. He} and \textit{P. J. S. Shiue}, Int. J. Math. Math. Sci. 2009, Article ID 709386, 21 p. (2009; Zbl 1193.11014)

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