Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials

Tian-Xiao He, Peter J.-S. Shiue, Tsui-Wei Weng

Research output: Journal ArticleArticlepeer-review

Abstract

Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known formulas of the Fibonacci, the Lucas, the Pell, and the Jacobsthal numbers in terms of the generalized Gegenbauer-Humbert polynomial values are given. The applications of the relationship to the construction of identities of number and polynomial value sequences defined by linear recurrence relations are also discussed.

Original languageAmerican English
JournalISRN Discrete Mathematics
Volume2011
StatePublished - Aug 2011

Keywords

  • Sequence of order 2
  • linear recurrence relation
  • Fibonacci sequence
  • Chebyshev polynomial
  • the generalized Gegenbauer-Humbert polynomial sequence
  • Lucas number
  • Pell number

Disciplines

  • Applied Mathematics
  • Mathematics

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