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

Tian-Xiao He, Peter J.-S. Shiue

Research output: Journal ArticleArticlepeer-review


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.

Original languageAmerican English
JournalInternational Journal of Mathematics and Mathematical Sciences
StatePublished - Sep 2009


  • Applied Mathematics
  • Mathematics

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