Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials. (26th October 2011)

• Record Type: Journal Article
• Authors: He, Tian-Xiao; Shiue, Peter J.-S.; Weng, Tsui-Wei
• Other Names: Liu W. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2011(2011)
• Publication Date: 2011-10-26
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2011/674167
• Languages: English
• ISSNs: 2090-7788

Abstract

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.